Your regular tricep exercises may get the job done in the short term, but long term progress requires some measure of variation. Here are six exercises that are proven effective -- you may know some, others may be new, but mixing things up is the best short cut to strong triceps.
While not explicitly stated, all these exercises assume that you keep your abs tense at all times for proper back support.
Most gyms have dip bars or a dip machine. If you don't have access to either, setting two sturdy chairs about 1.5 feet apart with backs facing each other works just fine. Either way, hoist yourself up so that you support your bodyweight on your hands. Bend your knees and cross your ankles for balance. Slowly descend, leaning slightly forwards while keeping your abs tense. Focus on triceps; you're using both chest/shoulders and triceps in the exercise, but you'll be surprised about to what extent you can control which muscle group is used most.
Cable Pushdowns (aka. Cable Pressdowns)
Stand in front of the pushdown machine with a short bar attached to the upper pulley. You may use a straight or angled bar, or a rope; whatever feels ok for your wrists. Place your feet about shoulder-width apart, knees slightly bent for balance, and your back straight. Shoulders should be a neutral, relaxed position with your elbows firmly tucked against your sides at all times as you push the bar down to a full contraction.
Overhead Tricep Extensions
Assume a position similar to the cable pushdowns described above, except you attach a rope to the lower pulley and stand with your back towards the machine. Elbows should point up but remain as firmly stationary as before. You may have to lean forward a little for balance; that's ok, just don't do any swaying while doing the actual exercise. While these extensions are great for accomplishing a full stretch and full contraction, expect to be a tad weaker so start easy.
Close Grip Bench Presses
Lie down on a bench as you would when doing regular bench presses, except assume a narrower grip (about a foot between thumbs) and bring the bar down to your lower pecs. Squeeze your scapulae together and keep your shoulders against the pad to keep the focus on triceps rather than anterior deltoids.
Lie down on a bench with your head just by the edge and a barbell held above your forehead with straight arms and a semi-narrow grip. Slowly let the barbell down towards your head, making sure to keep your elbows pointing straight up. As you achieve full stretch, push back up to the starting position. Note: some people prefer to do this with a cambered bar (EZ bar) as it's easier on the wrists. While one of the most effective tricep exercises around, also note that "monkey grip," ie. putting the thumb on the same side as the rest of the fingers, is not recommended unless you have a burning desire to find out how this exercise got its name.
One Arm Dumbbell Extensions
Sit straight up, legs apart and feet firmly on the floor for balance, with a dumbbell up above your head. Bend your elbow, slowly letting the dumbbell descend behind your head before you make a distinct turn and push the dumbbell back up. Keep the elbow stationary the whole time -- you may put your spare hand on your upper arm for extra support.
Closing Thoughts on Variation
The philosophy of keeping the muscles guessing by mixing things up applies not only to the exercises, but the poundage and number of repetitions as well. If you always choose a weight that you can do 10 strict reps with, your body tends to get used to that. Once it feels comfortable that it can handle this predictable workload each week, why would it improve?
While switching exercises around goes half the distance, go for broke by alternating high reps with low weight (ie. 12 to 20 reps) and low reps with heavy weights (six to eight reps). A note on the latter portion: this is assuming you've reached at least intermediate level, as you need to have some experience and feel comfortable with proper form before safely tackling the low rep/heavy weight weeks. Having said that, you have nothing to lose and everything to gain from keeping your muscles on their toes. Good luck!