I was thinking of building my own MVC system with a member system. However, I will need forums and I thought maybe I will just use the forums as registration and let that handle the members, but is there a better solution to wanting both an MVC system and forums?
I can't see any reason why an MVC centric approach would be incompatible with developing a forum.
Is your member system a particular model within your MVC architecture? If so, I think that would be a good way to go. This way, if you want to add more functionality (ie, blogging) that needs per member permission/authentication could draw from the same users Model.
Otherwise, the best solution is the one already written. CakePHP is pretty popular as a PHP MVC framework. Making forums with it shouldn't be too difficult.
Honestly, my answer is: Don't develop a forum, but take one of the many available PHP implementations and put your energy in theming it. I know this is not what you were looking for, but if you don't really have a completely new idea how forums should work, there is no point in starting from scratch.
But back to your question: Yes, MVC should work, even though you are probably going to mix view and controller a little bit in your code. But as @ford already suggests, it is worth looking for frameworks so that you can concentrate on the unique features of your forum.
Symfony provides a php framework. Takes more development time but provides greater flexibility.
There are lots of CMS's out there provide user management with forums available out of the box or as plugins.
There are lots of forums which can manage users and potentially you could extend to provide your desired other features.