My ex is in a new relationship and we both still like each other. He doesn't want to hurt her by breaking up with her, so he says we can start talking again when they break up. Should I try to break them up, or leave it be?

Something's not right here - if your ex is still interested in you, then why did he enter another relationship and why is he reluctant to end it? Especially if he was the one to initiate the breakup between you two; he knows that breaking up at any point is going to hurt this girl, so his explanation doesn't line up. (Even if he didn't initiate it, chances are good you were unhappy in the relationship - remember, there's a reason he's your ex.) From an outsider's perspective, it looks like your ex is stringing you along, so it might be better to let go of him and pursue other relationships; he's dating another girl while essentially telling you "maybe later", and that's not fair to you.