I have used SOOP Portal in the past. This is ASP based, using either Access or SQL database. Although the next version is still going to be written in ASP, it is supposed to have a MySQL option which would make it easier/cheaper to find hosting for it. I am not using it now because I couldn't afford the ASP/SQL hosting anymore. 🙁
I have heard rumors that support for Invision is not all that great. I don't know if it's true or not, but I have seen it posted in more than one place, by different people.
I have been testing phpBB at the moment, but also like what I have seen of the Simple Machines offering as well. For me it's a toss up between them at the moment.