People often stretch the definition of the term "corruption." The use of political office for private gain is the strict definition, where there is bribery, extortion, cronyism, nepotism, and other related quid pro quod.
This is confusing because in general "corruption" can mean basically any immoral activity. Also, some of the least corrupt governments in history have been some of the most brutal (though I am unsure whether this is merely the exception to the rule or what).
So, in the US, is there corruption in the strict sense? It's rare. It's more common in state and local governments, but still rare. What goes on at the higher levels isn't as direct as all that. If someone really believes (or is made to believe through some kind of unforced persuasion) that building the local sports stadium (to use an example upthread) is good for the community and, well, it just happens to benefit other people too that I happen to be friends with, then is it corruption? In a lot of people's eyes, yes. To me it's a new kind of animal, and one that may be just part of democracy.
tl;dr I can't just go give a stack of bills in exchange for a specific vote in most places in the US, but I can use that same stack of bills to get people elected that will vote the way I want most of the time anyway.
