One of the things I think is so great about baseball is the access given to players. While I don't go to games for the other sports so I can't speak for them. Baseball is great for allowing people to go by teams dugouts and get autographs. The few games I went to in basketball I never saw one person getting autographs. While at MLB games I can't count the amount of people hoping for an autograph.
When we used to do the autograph thing it was always the visiting team. For some reason it seemed like the visitors are more than happy to show appreciation for their away fans. I remember a few times we got lucky, and were the only people around. Those times were special as I can recall two times players actually stayed and chatted for a bit. The few times we tried the Mariners no results were had. When we did see the home team sign it was total chaos. People shoving, and pushing anyone who dared get in their way, including small children.
With stories I've read from other online places. This isn't a common scene, atleast I hope not. We do need to keep kids in not just collecting baseball cards, but in collecting autographs as well. Too much craziness, and they will just figure the reward isn't worth the price paid to get that one autograph.
This is one of the charms with minor league baseball. Most teams in the Northwest League have two players at a table signing for a limited time. One team we saw had an entire area for autographs with players coming over whenever they wanted. The best by far though is the collegiate team we have locally. At the end of every home game they allow families on the field for autographs, photographs, and just general talking to the players. It's events like this that will hopefully keep the next generation in these hobbies.