There are a few times in US sports where there are chants directed at other teams, particularly in Boston, where the population tends to be younger and drunker. The most famous was in the NBA Eastern Conference finals some time in the 80s. Boston was losing to the Philadelphia, and the fans started chanting "Beat LA", encouraging Philadelphia to in the finals against LA, who were Boston's major rivals. I think it's not uncommon at Red Sox games to do some anti-Yankees chants, just for the heck of it.
There is also of course a lot of stuff more localized to bleacher seats that doesn't involve the entire crowd. I know at SF Giants games, in the outfield, there is always a call-and-response chant "What's the matter with _____?" "He's a bum!" about the nearest outfielder. This is also usually accompanied by general heckling.