StackExchange would be a great alternative to such services as GetSatisfaction. I noticed that fogbugz is using StackExchange as a tool for driving community questions and answers.
Is it possible to use StackExchange for your own product?
No. They had it for a while with version 1 of stack exchange. You pay 100 bucks a month or something like that and you get a stackexchange with your name and logo. However, they realized their original goals weren't being met with that model so they changed their model with the advent of area 51 and the proposal's etc...
There are open source alternatives that have essentially copied the stackoverflow/exchange software you can use.
Here is one of the more popular ones.
Yes. For example, Google's Android uses stackoverflow.com as their official support forum. Wordpress and Apple also have StackExchange sites.
But your product would have to have enough of an audience to go through the area51 process. If you only had a small niche product that wouldn't support it's own site, and wouldn't fit as a tag on another site, then you'd have to use one of the clones.
Alternatively if you wanted to run a private instance on your own premises that the public would not have access to, we offer an enterprise version, but it's pricey.
If you're looking for a simple php mysql Q&A board with voting and gravatars, try http://www.question2answer.org Development has progressed significantly since beta in the fall. You can integrate it with an existing user database as well.