Size Matters
When it comes to runway length.
And wouldn't you just know it, but even runway length is subject to a variety of terms, and is the basis of several FAR's .

FAR Landing And Takeoff Field Lengths

"The FAR landing and takeoff field lengths ... contain certain built-in safety margins to allow for unanticipated
situations. Brief and somewhat oversimplified descriptions of these distances for dry, hard-surface, level runways in zero-wind conditions are given below." (Airworthiness Standards: Transport Category Airplanes," FAR Pt. 25)
Landing Field Length

"The landing field length is defined by the Federal Air Regulations for transport-category aircraft. Briefly, the landing distance is measured, horizontally, from the point at which the aircraft is 50 feet above the surface, in steady gliding flight at an approach speed not less than 1.3 times the stalling speed, to the point at which the aircraft is brought to a complete stop on a hard, dry, smooth runway surface." (Airworthiness Standards: Transport Category Airplanes," FAR Pt. 25)
"The FAR landing field length is obtained by dividing the measured landing distance by 0.6 in order to account for the possibility of variations in approach speed, touchdown point, and other deviations from standard procedures." "Certification and Operation: Domestic Flag, and Supplemental Air Carriers and Commercial Operators of Large Aircraft," FAR Pt.121, paragraph 121.195

Takeoff Field Length / Balanced Field Length

"The FAR takeoff field length, often called the FAR balanced field length, contains certain inherent safety features to account for engine failure situations. This takeoff field length is defined in several slightly different ways... Briefly, if an engine should fail during the takeoff roll at a critical speed, called the decision speed V1, the pilot is offered the option of two safe courses of action. He may elect to continue the takeoff on the remaining engines, in which case, the takeoff distance is defined as the distance from the point at which the takeoff run is initiated to the point where the aircraft has reached an altitude of 35 feet. In the second alternative, the pilot may elect to shut down all engines and apply full braking."

"The decision speed V1 is chosen in such a way that the sum of the distance required to accelerate to V1 and then decelerate to a stop is the same as the total distance for the case in which the takeoff is continued following engine failure. If an engine should fail before V1 is reached, the aircraft is usually brought to a stop on the runway; whereas, if an engine fails at a speed greater than V1 the takeoff is continued. The distances are based on smooth, hard, dry runway surfaces." "Certification and Operation: Domestic Flag, and Supplemental Air Carriers and Commercial Operators of Large Aircraft," FAR Pt.121, paragraph 121.195

OK, enough of the dry stuff, let's talk about getting it off...and on.
As you can appreciate from the above FAR's, we won't be talking about Transport Category aircraft in the following situations. This will be orientated toward the fun aircraft to fly- the General Aviation variety. When operating these aircraft you will inevitably come across airports that will demand the maximum performance of your aircraft. Factors that could be a consideration are trees at the end of the runway, snow, rough fields, short fields, and others. Let's pick away at these one at a time.
As an aside, I am a strong believer in not abusing your aircraft, or it's powerplant(s). However, unusual situations call for pushing your aircraft to the edge. Having said that to help clear my conscious, let's have at it.

Normal Takeoffs
As a foundation for the special operations to follow, let's go through a normal takeoff and landing, using our Speedmerchant 500 twin-engine General Aviation aircraft.

As you approach the departure end of runway 29, your checklist is complete and you are cleared for takeoff. You roll onto the runway in a gentle turn and apply full power to the Speedmerchant 500. Takeoff roll is normal, and you lift off some 3,000 feet down the runway. In profile, your departure looks like this:

Well, that's not bad, and that's the way that most folks do it, but look at the displaced runway area that you left behind. Why not use that for takeoff? It's legal, and it certainly makes for a safer operation. A couple of points though when you do this. If it is a tower-controlled airport, make certain that you advise the tower when you call with your "ready for departure" radio call. Say something like "Oxford tower, 57 Golf is ready for departure runway two nine, we want to back-taxi and use the full length for departure." The tower does not expect you to back-taxi, and they may have issued your takeoff clearance based on the timing of landing aircraft and your using the "normal" runway departure. Not telling them can create anger up there in the glass booth- and some heavily censored radio transmission directed to you. If you are operating at an uncontrolled field, always make a "blind radio call" when taking the runway using the CTAF- Common Traffic Advisory Frequency- for that field. Something like "Oxford traffic, Cessna 57 Golf is taking the runway, runway two nine for departure, Oxford." If you are going to back-taxi, insert that in your call.
There is an old saying in flying: There is nothing more worthless than the runway behind you, or the altitude above you. Use all available runway for every departure.
Short-Field Takeoffs
The runway surface is OK, it's just short. Obviously, someone flew the aircraft there in the first place, now it's your job to get it back out again. First off, consider departing in the morning when the temperature is usually at its lowest for the day. Also, consider using a lower fuel load, of off-loading passengers, baggage or cargo.
Taxi out to the end of the runway. I mean the end of the runway. In a best-case scenario, the tail of the aircraft will be hanging off of the end of the runway. If there is an over-run at the approach end of the runway, use it. The same applies if there is a displaced threshold.

Check the area under the propellers. If necessary, get out of the aircraft and clear the area of any debris like rocks or small stones. If you don't, these will be pulled up into the propeller arcs when you apply full power causing a ding in the blades which can lead to blade failure.

A "ding" in a propeller blade creates a stress area in the metal. Usually, these "dings" occur in the outer 1/3 of the propeller blade where the most stress is. In a worst-case situation, the stressed area will crack and the portion outside of the crack will separate from the propeller. This causes an incredible amount of vibration. This vibration then puts more loads on the engine mounts than they were designed for. In many cases the engine is torn off of the engine mounts before the pilot can say "What the.....?"

Here's our runway:

Airspeed nomenclature
There are a couple of airspeed terms that we need to understand here.

Best angle of climb airspeed
This airspeed will put the aircraft into the air at its steepest angle- this is what you want to use on a short-field takeoff.

Best rate of climb airspeed
This one will give you the best rate of climb, but the angle will be less than when using best angle of climb. In other words, you'll gain more altitude per minute but will cover more ground in the process.
Both of these airspeeds will be in the aircraft Owner's Manual.
Back to our short-field takeoff. You're at the end of the runway. Set the parking brake. Stand on the toe brakes. Bring up full power smoothly, but smartly. When the engines have stabilized at full power, disengage the parking brake, release the toe brakes, and roll. When you reach the Best Angle Of Climb airspeed pull back on the wheel and hold that airspeed. Go any slower and your rate of climb will decrease, go any faster and your angle of climb will decrease. Try not to turn the aircraft. Banking (turning) is inefficient from an aerodynamic standpoint, and it will decrease your rate of climb. Of course, if you're trying to avoid a hill straight ahead, and head for a valley you have no choice.

Short-Field Landings
We'll look at two landings here: one with obstructions at the approach end, and one where the approach area is clear.
Here's our first runway:

In a perfect world, you would make every landing at an airspeed of 1.3 times Vso, "stall speed, power off (with appropriate flap setting)." However, there are short runways out there, and many of them have obstructions at the approach end. So, in this case, you will need to hang your behind out in the breeze a little. Your approach speed will be slightly above Vso, perhaps 5 to 10 knots. If it is turbulent out there, add one-half of the wind gust speed to your approach speed. In other words, if the wind is 20 knots, gusting to 30 knots add 5 knots to your approach airspeed. You will need to be well set-up in advance for this approach You should have the aircraft set at the descent angle and at your target airspeed at least one mile from the runway. Establish your airspeed with full landing flaps. Add power as necessary to hold this speed Look at the end of the runway. Notice where it is in relationship to the nose of the aircraft- this is important. If the runway end is moving toward your reference point, you will overshoot the end of the runway and land long. If the runway end is moving away from your reference point, you will land short and do a little tree trimming. This is a difficult landing, and requires all of your skills as a pilot. If at any time you are uncomfortable with how things are going, break off the approach and set-up again. Also, if there is any wind, expect an "air bubble" as you cross over the tree. It will normally push you up a little bit. Once you cross over the tree, do not reduce your power- it got you this far, it's going to get you to the end of the runway. If you decrease power prematurely you could very well stall and drop the aircraft in. Just before touchdown, or immediately after touchdown, chop the power. Reach over and raise the flaps. Don't be hasty and grab the gear handle, it's been known to happen. Start heavy braking. Raising the flaps will transfer more weight to the gear, and make your brakes more effective.
Here's our second runway, with no obstructions at the approach end.

Hmmmm, notice something familiar here? With the exception of no tree, and no displaced threshold, it's the same as the one above. Why would you want to come in at the same approach angle as you did when clearing an obstacle, the tree? Why not "drag it in" at a shallow approach angle and just chop the power when you touch down? Good question. So, why? Ah, Grasshopper, physics. Let's see what factors are in play as your aircraft approaches the runway and you touch down.

Notice the "forward motion to dissipate after touchdown". This directly relates to your groundspeed at touchdown. Notice that when "dragging it in" all of the airspeed is forward, and that when using a steep angle of descent some of the airspeed is forward, and some is vertical, due to your descent. The forward motion is less when using a steep angle of descent, and you will be able to stop on the runway in a shorter distance.
And that, Grasshopper, is why you don't want to "drag it in" on a short runway. Pretty neat, huh?

Rough-Field Takeoffs
Let's say that your departure airport is "rough as a cob". The length is OK, it's just a very rough surface. Position yourself at the end of the runway, and set the flaps for the maximum deflection for takeoff. Hold the brakes and bring up full power. So far, with the exception of maximum flap extension, this is pretty much the same as a short-field takeoff. Pull the wheel full back, right into your stomach. Disengage the brakes and start your roll. Holding full back pressure on the wheel, allow the nose to raise off of the runway as soon as possible. Once the nose comes off of the surface, ease up on the wheel so that the nose remains off of the runway but the aircraft doesn't continue to pitch up. If you allow the nose to clear the runway any more than is necessary the aircraft will create considerable drag that will only lengthen your departure distance. The aircraft will lift off and start to fly prematurely because of ground effect- that "air cushion" near to the ground. For all intents and purposes, ground effect comes into play vertically from the surface equal to the aircraft's wingspan. It is more pronounced in low-wing aircraft than in their high-wing brethren. This is an area where you have to exorcize considerable caution, as if you try to climb out of the ground effect the aircraft may stall and settle back down onto the runway. Allow the aircraft to accelerate while flying just above the runway. Once the aircraft is at a safe airspeed, initiate a shallow climb. When the aircraft is at least 500 feet above the ground, and preferably 1,000 feet, slowly retract a notch of flaps. The aircraft will settle a little bit when you do this. Allow it to stabilize, and continue to slowly remove flaps in stages, waiting each time until the aircraft has stabilized before proceeding. Pay particular attention to your airspeed throughout this exercise. After all of the flaps have been retracted, and the aircraft is stable, proceed with a normal climb out. Rough-Field Landings OK, you got it off, let's put this baby back on. Now's your chance to drag the airplane in, unlike the caution not to do this in short-field landings above. Approach the field in a shallow glide path, with full landing flaps deployed and sufficient power to maintain airspeed. As you cross the end of the runway, slowly decrease power but do not remove it entirely. Ideally, what you want to do is have the airplane slowly settle onto the runway at minimum flying speed. At touchdown you should have the wheel full back to the stops, buried in your stomach. As soon as the plane touches down remove all power and continue to hold the wheel full back. Leave the flaps extended as they will lighten the weight of your "footprint" until you slow down. When taxing back in, continue to hold the wheel full back to lighten to load on the nose gear.

Snow on the runway
The amount of snow on a runway that your aircraft can handle is pretty much directly related to the size of your tires, and therefor the size of your aircraft. It doesn't take much of the white stuff to make just moving on the surface of the field almost impossible. Any more than a couple of inches of snow and most smaller aircraft simply cannot accelerate to a speed fast enough for lift off. On landings, the snow will "grab" the mains and tend to slam the nose down prematurely. Unless it's just a light dusting, you are better off to wait until the plows have cleared the field- or June.

Ice on the runway
Ice is not as bad as snow- in some respects. If there is any appreciable crosswind it's not a good idea to try either taking off or landing. If the wind is down the pipe or calm, you can give it a shot. Keep in mind, of course, that your braking abilities will be almost nil, and that if you have to abort your takeoff your landing gear will most likely be removed as you proceed through the airport fence. Having said that, I landed in Minnesota on a glare ice runway in the 421B one cold February day. I was able to land at the end of the runway, and never used the brakes during the roll-out. Any turning motion was countered by using differential power on the engines, as were all turns. Taxi speed was slower than a normal walking pace, and I seem to recall my butt hovering several inches above the chair.

Summation
You may come across situations that require combinations of all of the above techniques. The main thing is to understand why you are doing what you are doing, and how it effects the safe operation of your aircraft. Keep in mind that any time you are operating outside of the normal envelope you are putting yourself, and your aircraft, potentially in harms way.
Fly safely.

Stoen, Hal. "Getting Off...............And On." Stoenworks. June, 2002. Stoenworks. 21 Jan 2008 .