If I have people adding reviews and stuff on my gaming site, and posting on my forums, should I have something that says all content they submit becomes my property or something?
I would. But before I would do that, I would check, do I want to "own" or do I want them to "own" it? If they owned the posts, then I can remain an ISP, and have to manage it in a limited fashion, and have less liability head aches. If I owned the posts, then I can do whatever I want to with them, even republish it in an e-book. Of course, it increases my liability.
Check with your forum's software. In most cases it clearly stipulates that what people say on your forums becomes your property. Consider adding a disclaimer to mention that the "opinions of the posters are not necessarily those of the forum manager" too.
But if it's your property, are you also then personally responsible for it? What if someone posts something illegal? An unlikely scenario, perhaps... but stranger things have happened.