Yep, usually drugs, or mistreatment of horses. Owing USEF money (not paying entry fees, membership fees, etc) is fairly common as well. You're not allowed to show until you pay back that money. Any breaking of major rules, particularly competing in a division you aren't supposed to be in (professionals in amateur divisions, showing in a green division on a horse that is not green eligable, ponies not in their proper height division, etc) is considered an offense.
Usually you're tried before a committee and they fine you and possibly bar you for the rest of the show season. I think after 3 offenses you're suspended.
If you ever get a chance to read the Equestrian magazine (USEF's magazine that you get if you're a member) they have a list at the back of every issue of the people who were suspended and why. It's awesome! I'm glad they publicize te people who break the rules!