Where do you put a book trailer for maximun exposure?

I would definitely put it on YouTube.

If your book is being sold by Amazon, you might want to look at putting it there as well. I've no idea what the requirements are, but I have noticed an increasing number of trailers pop up on product pages.

That would depend on your genre and the type of story it is. Then, you need to research websites where people who you think would like your book (your "target market") goes regularly and that they would consider trustworthy and find a way to either advertise on the website (the owner might be willing to put up a link to your trailer if you ask nicely and they think it sounds interesting) or post in forums dedicated to what you write about. It's important to target your publicity because if you post everywhere indiscriminately, you'll look like a spammer

If you have a blog, you might want to put it there and ask friends to post it on their blogs. Also, Facebook. I would send the URL of the trailer on YouTube to anyone online who might be writing a review, as well as emails with the URL to as many as possible in hopes of spreading the word.

You could also look for blog posts that discuss trailers and leave a comment (make sure it ads something to what they posted).

I've done posts about book trailers I like and I've asked others about their own book trailers in interviews I've done. I know I'm not the only blogger who has done so. You can also leave comments on trailers on YouTube.

I agree with Kathleen. I've posted on Youtube and then put a link to it in my signature so people can easily access it. My novel is YA UF so I've linked up with sites associated with teenagers and hip things like twitter, facebook, myspace, and blogs associated to twilight and new moon since that is happening for kids right now. Good luck!