Amazon.com offers an associate (affiliate) program that can be used by forum owners to monetize their forum. Reports I have read from forum owners on this are mixed. It will work on some forums and not on others. In some niches, people are more likely to buy books or the types of products that Amazon provides.

How to integrate Amazon into a forum:

Generic banners are probably not going to work too well unless they are closely related to the niche.
Specific product links (eg a new book that has just been released) related to the niche are more likely to work well (I do a monthly search at Amazon.com to look for new releases related to the niches of my forums).
An aStore with a comprehensive selection of products related to the niche could be inserted into the site and linked to from the forum navigation bar.
Occasionally I do a special promotion from Amazon for a generic product (keep an eye on the Amazon Associates blog for holiday promotions), but usually the results are mixed (I did a blast across all the forums for Windows7 from Amazon when it was released and it was a dismal failure). It is easy if using something like OpenX, as you only need to create one advertisement and then it gets delivered to multiple zones on multiple sites (if you have them).
On a couple of forums, I have set up a book subforum which is for discussion and reviews of a new book. The first post is about the book from the publisher; an image of the cover; and links to buy the book from the different Amazon’s. The second post in the thread will be a highlight of a couple of readers reviews from Amazon – hopefully this stimulates some discussion. I always email the author with a couple of questions and post the answers. This serves two purposes – it provides more information on the book and tries to get the author engaged with the rest of the forum, as they are probably an important person in the niche (it is all part of the plan!).
I also use books as the prize in some competitions and drop the affiliate links to buy and the book in the competition thread. I also invite the author to judge the winner of the competition (it is all part of the plan!).

Where to place Amazon advertisements:

Link in the navigation bar to an aStore
Top banners work so well with Adsense, I do not put the Amazon ones there.
I mostly use specific product links in on the side of the page – I use OpenX to rotate several 120×240 product links (I use the Ultimate Side Columns modification for vBulletin).
In a book subforum for discussion of the book
In competition threads where a book is the prize.

Amazon run several country specific divisions and you have to sign up for each individually if you want to earn commission from them:

Amazon.com
Amazon.ca
Amazon.co.uk
Amazon.de
Amazon.fr
Amazon.jp

I belong to them all and use OpenX to geotarget which advertisement is shown based on the country of the visitor. Its a bit silly only belonging to Amazon.com if a lot of your visitors are not from the USA. See my posts on the books: Managing Online Communities, Twitter Wit, What Would Google Do? or Art of SEO, and the geotargeted advertisement at the bottom of those pages.

I also belong to the affiliate programs of Fishpond (Australia) and Fishpond (New Zealand) for books from those countries as Amazon does not have an office there. The advertisements from them are geotargeted via OpenX to just Australia or New Zealand. I have looked for affiliates in other countries not served by Amazon, but have not found any that I am comfortable with.

I'm not sure about all of them but I know "Art of SEO" is in an ebook collection I posted and is a good read.