I've maybe done more than 50, and that was a long time ago. 30 or so is probably more realistic now. I normally do sets of 10-20 depending on what routine I'm doing. I've nr understood how people could do so many pushups in a single set, even when they're not doing deep/full-range ones.

Practice. Slowly working one's way up to bigger and bigger sets. 

Wow, a lot of fit people here! I thought I did pretty good with 45, but when I see people managing 70-80 or not to mention 100 I go @_@

I've done 80 a few times but I imagine my form was pretty bad so I'll say 60-ish.

If it was a challenge or for money maybe 50 or so. My triceps will always exhaust themselves way before my chest does though. I never really do excercises with more than 15 reps of anything, because the weight would be so low that it doesn't really stimulate the muscle to grow (or not nearly as quickly). 

For chest I just do basically just the meat & potato excercises -- bench press, flys, cable crosses, dips, for chest but push-ups ... probably haven't done those regularily since I was a kid.

Push ups, pull ups, things like that ... any one can gradually build up the ability to do a ton of reps though, even if they're scrawny, eventually it becomes easier and easier if you do it daily. Might be a little harder if you're obese, but I find fatter guys can bench press a ton in some cases. 

My record is 100, but I swear I couldn't do even one more.
Felt a little sore the next day too, I wanted to do them as fast as I could, but I'm not used to long lasting, intense effort...