I've never caught a baseball at a game, but I've had plenty hit in my general direction. Whenever one comes my way, I tend to freeze, focus on the ball and hope I catch it if it comes close enough. I had one land literally two seats away in spring training a few years ago.
That's just me though. At Thursday afternoon's Blue Jays-Tigers game, some guy in the crowd managed to snag a foul ball while talking on the phone without ever breaking away from the conversation. To the action footage:
He snagged the ball in a crowd of people, too. That's rather impressive. Great ballhawking skills, unlike yours truly.