I can see Joe's point about "Thank you in advance" being manipulative. I don't usually use it in English, but occasionally I'll tack a "Danke im Voraus" onto the end of a German e-mail, but only in specific circumstances and usually only in German e-mails because it seems more common to use it in German than in English.
I agree that saying thank you in advance means it's a foregone conclusion the person will do as you have asked, i.e. they have no choice in the matter. For that reason, I would think it's a little impolite to use when you're asking someone to do something they could very well refuse. For example, let's say my car has broken down so I have to take it to the shop and I won't have a car for a while. I could write an e-mail to a co-worker saying "I won't have a car Friday afternoon, could you please drive me home from work?". In that case, I think saying "Thanks in advance" would be presumptuous. The co-worker is under no obligation whatsoever to give me a ride, in fact it might be terribly inconvenient for them or they might not even be able to. But by saying "Thanks in advance", I'm essentially saying "Thank you already because I know you won't say no", which puts them under pressure to do me a favor.
On the other hand, let's say I encouter a problem with a manual I'm translating. I could write to the author, ask for clarification or correction, and conclude with a "Danke im Voraus". In that situation, they don't really have a choice as to whether or not they are going to help me. They have to, because it's one of their job responsiblities and as the author, they are the only one who can help. In that case, it IS a foregone conclusion that they're going to help me, so I might as well be extra polite and throw in a thank you before they even do the task. And then when I get a response on the issue, I'll thank that person again. I don't view the advance thank you as a replacement for thanking the person later, I just view it as an extra thank you which seems a little nicer.
And I have to agree with the other native speakers who say "Thank you in anticipation" doesn't sound quite right. I won't say it's wrong, but I can definitely say I have never seen or heard it used and I wouldn't use it myself. In fact, if I did encounter it, I'd probably think it was said by a non-native speaker.