Clutch Slip - Any time the clutch is not fully engaged or disengaged when the car is running, it is slipping against the flywheel. As the clutch comes up and reaches the friction point it begins touching the flywheel, and they are spinning at different speeds. They must sync up and during this time the clutch is slipping. When it is slipping it is wearing. The clutch is designed for this purpose and it is designed to wear. But excessive and unnecessary slipping will reduce clutch life.
Upshift - Shifting up through the gears: 1 -> 2
Downshift - Shifting down through the gears: 4 -> 3
Throw - The distance the shifter moves between gears.
Engine Braking - When in gear and off the throttle the compression of the engine creates drag against the drivetrain and the wheels, slowing the car down. Lower gears provide stronger engine braking than higher gears.
Coasting
In Neutral: Rolling down the road with the car in neutral. This is generally an unsafe maneuver as you do not have total control over your car, because you can not immediately accelerate. In many places it is illegal. Coasting in neutral uses the same amount of gas as idling, as the engine must maintain idle speed to keep running in neutral.
In Gear: Rolling down the road with the car in gear but off the throttle. This will produce some engine braking. The engine is forced to run at it's given revs due to its direct connection to the rolling wheels. In modern fuel injected cars, coasting in gear above around 1500k rpm (different in different cars) uses no gas, as gas is not needed to run the engine due to the wheels driving it.
Lugging - When your speed is too low for the gear you are in and your engine is lugging or laboring to produce power, accompanied by an unpleasant sound and a shaking or shuddering of the car. This is not good for the engine or fuel economy.
Blip - Tapping the throttle during a downshift to rev-match.
Straight Cut - Many cars have straight cut teeth on reverse gear. This makes it harder to engage and produces a whining sound when traveling in reverse. This is normal. If you have trouble shifting into reverse, try first shifting into a forward gear, and then into reverse.
Synchros (Synchromesh) - These are cone shaped devices within the gearbox that sync up the speeds of the input and output shaft so the gear can engage. You can save wear on these if you double clutch but it is not really necessary in modern cars, the synchros are designed well and last a long time. If they do wear out you can work around it by double clutching.
Rev-match - Matching the engine/flywheel speed to the speed of the clutch, to reduce clutch slippage and have smoother shifts. Wait for the revs to drop when up shifting (or shift fast to get it done before they drop too far, I have this problem some times in my 6 speed). For downshifts blip the throttle to raise the rpms for the lower gear.
Single Clutch - General way of shifting modern cars with synchromesh gears. Clutch in, shift from one gear to another through neutral, clutch up.
Double Clutch - Bringing the clutch up in neutral during a shift. Double clutching is not really necessary in modern synchromesh cars but it can make things smoother and is fun. You are basically not only rev-matching the engine to the clutch, but also the input shaft to the output shaft between gears, doing the job of the synchros. For a double clutch downshift: clutch in, shift gear to neutral, clutch out, blip throttle (this is the rev-match for the input shaft to the output shaft), clutch in, shift neutral to lower gear, clutch up. If you do it fast enough the one blip in neutral is enough. If the revs fall too fast you can give a smaller 2nd blip before clutching up. Cars without synchromesh gearboxes require this maneuver. Double clutching is also useful for downshifting into 1st as many cars do not have synchros or have weak synchros on 1st gear.
Heel Toe - Braking and rev-match downshifting at the same time. Brake with part of the right foot, clutch with left foot, shift, blip throttle with right part of right foot while continuing to brake with left part of right foot, clutch up.
Bump Start - Starting the engine using the clutch and the momentum of the car. Get the car rolling, and put it in gear, 2nd is probably best, with the clutch down while the car is rolling, quickly release the clutch. This will spin the engine up. As soon as the engine is running clutch back in to avoid stalling/bucking/jerking/zooming off the road, etc. This is not a generally recommended technique but is useful if you must start your car and the starter is not working. Also, some people swear by this method for fuel economy via turning off the engine and coasting, and then bump starting when acceleration is needed.
Stall - We all know what this is. It sucks. It happens to everyone. It can be embarrassing. But it's not hurting your car so don't worry about it.
Bucking Bronco - When starting out from a stop in first you either released the clutch too fast, or gave too much gas, or both, and the car jerks and jolts, like riding a bucking bronco. It's painful and embarrasing but it happens to everybody.
Grinding - When you mess up a shift and hear grinding, it is not the actual gears in the transmission. It is actually the synchros. It's a bad thing and you want to try to avoid it, but doing it a few times every once in a while is not going to destry your car.
Power Shifting - Shifting with the throttle floored the whole time. You have to shift very quickly and this isn't recommended unless you really know what you're doing.
Clutchless Shifting - Just as it sounds, shifting without the clutch. You have to do it at the exact right revs and know what you are doing or it will grind and you have the potential of really messing things up. Not recommended.
Short Shifting - Shifting at low rpms to save fuel, as opposed to shifting at high rpms to maximize acceleration and power.
Rev Limiter - Cuts fuel to prevent going over red line when revving the engine with the throttle.
Over Rev
Throttle induced: Revving the engine past the redline using the gas pedal. You will bounce off the rev-limiter.
Mechanical: The engine is forced over the redline via being in far too low a gear for the current speed. The direct connection between the wheels and the engine forces the engine to spin too fast. The rev limiter can not help here and things can start getting very damaged very fast.
Power Band - The rpm range where your car produces the most power and has the best acceleration. If you want to have fun, keep it in this range

(Note: this thread was taken from a post by jomotopia. Thank you, jomo, for your lengthy contribution. It will be a sticky for all time.

Please feel free to add to this thread, as we're always coming up with new words and terms.