Asking for relationship advice on this forum usually brings out the most incredibly irrational and paranoid views on women. From most responses on here, you'd think that every woman was just waiting for an opportunity to cheat on you and that the only way to prevent this is to 'man-up' and tell her she either caters to your every paranoid demand, or you kick her to the kerb.
It would appear that she's chosen to be in a relationship with the OP and to be friends with her ex. Unless she has done something to make him think that she wants to be more than just friends with her ex, then the OP should have nothing to worry about.
Sure she might get back together with her ex, just like she might leave you for a random guy she meets somewhere down the line. Only you know your girlfriend well enough to know if you trust her not to do either of the above.
If you're looking to end an otherwise good relationship, simply because your girlfriend still confides in her ex, then I think you need to ask yourself if she's actually done anything to deserve this mistrust. Sure you might choose to trust someone who then lets you down, but don't let a paranoid fear, or irrational jealousy be what determines your decision. Based on some of the views, there's a lot of insecure people on these forums, who'd rather run early, than stick with something good and risk getting hurt. Only you know whether you are prepared to trust your girlfriend, whereas some people here wouldn't trust a girl who once had a conversation with another man.