I've used InvisionBoard, phpBB, and SMF over the years. phpBB is GPLed, and probably the most-used opensource forum script. It's also absolute hell to add mods into, requiring you to patch it's script files (even with AutoMOD). SMF isn't opensource, but it's a complete breeze to use. It also has plugin system, so modules are pretty much self-contained and easy to install and set up. As for IB, I haven't used it in a long long time, but from what I remember it was really good for huge huge boards, and seemed fairly decent.
As for that, if you don't want to think about FTPing or CHMODing files or anything else like that, like Tonepoet suggested, try a free forum host. You'll probably be pretty limited though, like you might not be able to export out your database if you ever want to set up your own standalone forum.
