Pitch counts are a very individually based subject. Of course the younger they are the less they need to throw.
How much do you throw during the week? I think the more often you throw the more you can throw in a game. That might sound like a no non sense quote but there's actually coaches in lower levels of baseball that think kids must totally rest between starts. Kind of like going out to the golf course and not even bothering with the driving range and you haven't played in a couple weeks.
I'd say your average kid that has a coach, father, brother, etc. that knows what he's doing would be able to pitch the following with out killing their arm:
Little League: 60-70
Babe Ruth: 70-80
High School: 90
That's just ballpark numbers. Your going to have kids that can throw 100 pitches and have no damage or pain due to their proper mechanics, then you'll have kids that can go throw 30 pitches and be in pain for a week.
Also, always, always, always, run after you pitch, even if the kid throws a complete game he needs to run sprints, poles, something. I personally prefer sprint because the pitching motion is much like a sprint. You go all out for a little bit. Many coaches believe in distance running, but I just don't think it helps that much when it comes to pitching.
You have to get your legs used to using maximum force at small increments at a time. Distance running does not do that.
This has gotten long, but the main thing is this. If you keep your arm in shape while you're young, when you're in High School and possibly college you won't be waking up at 4am with needle pains going through your arm.
If you want some specific workouts or regimens PM me.