I'm with Medusa in that I believe people can change....
I also believe that people don't ever really change for another person...they change only because they really want to, and are willing to do some seriously hard work.
For me it boils down to "actions speak louder than words" and this...
I've been in relationships that nurtured all the worst parts of me....jealous, angry, insecure, resentful, exhausted and pissy....and relationships that nurtured the best parts of me....caring, providing, nurturing, protecting and loving.
At this point in my life I don't know if that's because the first were crappo people while the latter were good....or if every relationship is a mirror, and what is reflected varies as each highlights different parts of who and what is already inside me.
I'm far from perfect...and I don't expect perfection in a partner either.
What I do insist on is that the person I'm with be fundamentally kind, always honest with me, and that the parts of me that reflect in that relationship mirror are those of my better self, and not my worst. If someone brings out the worst in me, then I need to go.