How many times does an answer have to be reported before it is removed?

usually just 2

but it can be one from a trusted reporter

Usually it is once by a very reliable reporter or twice by reasonable reporters. Answers which are in voting, resolved or are best answer can sometimes be a bit more difficult to get reported and removed successfully.

Depends on the reporters trust rating. A while ago we had an outbreak of people posting malware links. A group of users had an organised effort to delete them and the trust rating of these people went up. You could drop a posting with one vote. False reporting will lower that trust rating. So in fact it's an unanswerable question.

It generally ranges itself out. An answer/question can be reported 10+ times by beginner level 1 trolls who create accounts for the sole purpose of trolling/reporting unfairly, and the answer/question if asked or answered by a reliable, trusted user probably won't get shut down. Between reliable users with some reporting power, it usually takes 3-4 swipes.

I think its 3 times....

:]