well what can I say- +1! BMXs are probably the worst in my opinion, as you’re so low and they don’t balance nicely at all. Nor do they have feasable brakes for the job.
You need a medium height seat, mountain bike, the ability to flip the bike, and 1st or 2nd gear. I say 2nd gear as sometimes it helps to have slightly more speed in the wheelie (1st can be too slow, therefore you fall sideways).
Idealy, you’d angle your seat (using a bolt or screw, whatever is under your seat) as far forwards as possible (down, so you find it hard to ride the bike flat on the ground sitting on the seat) so that when you are in the wheelie, your mass is pushing down on the back of the seat and you are sitting upright, rather than having to lean right back holding on for dear life, about to fall off the back! (extremely long sentence there, I know ^^)
The most crucial point is the way that you use your back brake. It obviously needs to be fairly well working or the idea would not help. When you are up in the wheelie (with idealy your index finger resting on the back brake), pedaling steadily and start to fall back slightly (you need to make sure that if anything, you will fall back not forwards), you need to apply gradual force to the brake to bring you back forwards slightly. This is called brake control - key word there is control. You’ll need to get exactly the right amount of force on the brake at the right time and then you can always trust that you will not flip the bike - therefore the only thing stopping you is a ‘‘UPD’’ or your hands aching meaning you are obliged to go down.
Well to sum it up, that must have been my most long winded post yet thus I hope it is useful.
Here is my video of me wheelying my bike.
As you can see, once you can do it normally there are many variations that make it very fun to do. Another one not in the video is to take the front wheel off (once you’re experienced) - it makes it much easier, when you’re up, as the front half weighs next to nothing without the front wheel :D. Or even, you could go as far as unibiker did and fully convert your bike!
Finaly - a quite recent thread where some of this was discussed that you may be interested in.