The only reason I would go to a baseball game is for the atmosphere, I've learned it's fun to go just for that. I don't GAF about sportzing. So, I'd give the ball to a kid, but only if one nearby was trying to catch it, too. I wouldn't just hand it over to any random nearby kid, if they didn't even make an effort.

However, if I knew the ball I caught (like that would happen, me actually catching a ball) might have some value because of who hit it, etc. Then, I'd probably keep it. Assuming I caught it fair and square.