If you are credentialed for an event, it is certainly inappropriate -- and in some cases, explicitly banned in writing on the credential itself -- to seek autographs.
It's an abuse of your position and also jeopardizes the image of the professionalism of all other credentialed reporters in the eyes of the athletes you're covering.
A credentialed reporter has access that the general public doesn't have, and that access is based on him or her doing a job, not using it for personal gain.
I knew a minor-league baseball stringer who used to bring his card collection to games he covered. Lots of guys told him to buzz off, but some signed.
Occasionally, you might get asked to get autographs for kids (your own or others), and if that's the case and you absolutely have to do it, it's probably wise to go through the team's PR department.
I think it's a little trickier if you're at a banquet, say, and somebody is the guest speaker. Often there's no credential involved, and some cases, you might have had to buy a ticket to get in. I still wouldn't do it, but it might be a little more kosher than doing it at a credentialed event.
What if you're interviewing someone at a signing event? Well, here again, if you pay the fee to get in, I suppose you could make the argument it's OK to get autographs. I think if they let you in just to talk to the subject, it's probably off-limits.