regularcat, Fili has hit the nail on the head. A big part of why people don't like Americans is because of their ignorance of the rest of the world. It's often got little to do with the government.
It is a good question though Shifty, and has made me think. On my trips to SE Asia I've actually found the average Brit much ruder and lower. Americans are generally very polite overseas, where as Brits get absolutely wasted, are demanding, abusive etc. That said, I think this is swayed a little by the Americans that travel to SE Asia. It's quite a way for them, so they're generally people that want to travel for what I see as the right reasons-to experience people, culture, food and places. It's halfway to Australia for Brits, so is loads of backpackers looking for a cheap place to get wasted on the way home.
However in Europe it was another story. Americans used to drive me crazy. So many of them were clueless about not just the places they visited, but the cultures, the customs, seemingly even the way other little thought.
That said, in London (and Thailand among other places) I cringe at the typical loud mouth obnoxious Aussies. They're loud, drunk, and ignorant. A few of the worst aspects from both of the other two. Our reputation from what I know, is still a little better in mainland Europe, but in London they often called us JAFAs (stolen from the Kiwis for an Aucklander) for Just Another ******* Aussie, and some called us New Yankies. Even loads of Aussie hated them (for the two they gave us), and used to call them Walkabout Aussies - making they were the type of Aussies to go around the world to drink and hang out with other Aussies (at Aussie pubs like the walkabout).