1) vBulletin is the best paid, but it's worth going for it is you will be using all the multiple nerd knobs, which is something that not everyone needs, has great community support and there are lots of mods made by users.
2) phpBB - free stable forum script. Lots of good and heavily populated forums exist on phpBB.
There are excellent phpBB hosting accounts from Serverpoint.com, Siteground.com, Webhostingbuzz.com.