I use SMF for a private forum I run, and now I want to use it on a website I am creating. I like it a lot, and I think it looks quite professional.
Personally I use SMF on my site cause it's really easy to customize and it's free. Although I find Vbulletin as a very good forum software and wouldn't mind having a license for it and I would recommend it for someone who can afford it. I've tried using a lot of forum softwares but the only thing I know how to install and edit is SMF. IPB is quite good too but I think they lack in features and versatility. SMF is awesome because you can basically get concept from other softwares like Vb and IPB and convert the ideas to an SMF mod and your SMF becomes a compilation of different features from different forum software and to top it off, you can get Vb themes available for SMF as well. XD
I use SMF, best software out there Im thinking of coding my own software for my forum/tutorial site though.
PHPbb3 is great for small or new communities, but VB3 is definitely the best forum software out there Invision is good, but VB have just streaked ahead with 3.7 and it's new features. xD