I do not know how high I can jump, but what I do know is that I want to jump higher. It is one of the things I just can't seem to improve upon.
CsfanNH
Ok: Some things that really helped me.
First of all, stretch a lot. If you don't know basketball stretches, look them up. Stretch before you play ball, and if it's near the middle of the day, try to stretch afterwards. If it's later in the day, just wait. Every night you want to stretch before you go to bed. This gave me 2-3 inches on my vertical very quickly. I was really surprised but it worked for me.
Wall sits. Stand with your back to the wall, and put your feet almost shoulder width apart, then crouch until you are in a full sitting position, like you're in a chair.
Make sure your hands are above your head or something, just not touching your legs. Stay there about a minute. I do this once a day, but you can do it every other day or whatever.
Calf raises. Stand with your legs, again, about shoulder width apart, and then slowly (not too slowly) stand up as high onto your toes as you can, and again slowly back down. Do this about 30-50 times, and see how tired your legs are. Use this to gauge how many you should do normally. You can do this every day, but I wouldn't recommend it until you've done it every other day for a while. It's a very hard workout to keep up every day. If you want an extra edge, do it on a set of stairs or some other object (I use textbooks if I don't have stairs) and go down below your natural standing point (you stand with the balls of your feet on the object and then the back of your feet go below the edge of the object/stair step).
Also running, biking, and jump-roping help. Running stairs helped me, but that's really hard.
If you can, try to use a leg-press as well. They're pretty effective.
Hard work and diligence will get you there, man. Also trying to get as thin as you can (without becoming too thin, obviously) will also help. I'm naturally very (very, very, very) thin, so this process was a little easier for me than some people.