I installed and tried in the past:

1. PhpBB Forum
2. Simple Machines Forum
3. Yabb Forum

I liked Yabb and simple machines the most (personal choice). Anyway I prefer and use eBlah. Why?, well, it has RSS functions, self archive, ban tools, its free, it support several themes and languages and self backup, it also has pms and news functions. It includes a way to insert the last posts in any page of your site vía JS.

I know its arguable, but I like it because it doesn't require MYSQL. This makes it easier to move from server to server and deal personally with its internal data exchanging with other apps. I can just zip the directory and expand it elsewhere with no hassle, except from 2 or 3 settings.

I tried the other options but I didn't enjoy moving the forums from server to server.

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