Should I break up with my girlfriend or marry her?

Wow... First, the fact that you are wondering if you should dump means you probably aren't ready for marriage. Second, you say you want to date other girls. I say that you don't really want to be with her. For her sake, dump her. Let her find someone who appreciates her and wants to be with her. Also, for your sake. You deserve to be with someone that you want to be with and aren't having second thoughts about.