Besides the values you mentioned (communication etc), I don't have a specific list... I've always been the "go with the flow" type... and if the flow stops going, I take a step back and evaluate what's wrong. If it's something that can be fixed, I try to fix it. If it's a deal-breaker, I break the deal.
The other question is easier for me to answer: A relationship is successful if it's good while it lasts and ends on positive terms if it ends at all. If a relationship is more work and heartache than fun and happy, that's not successful.
I used to think I could never date a smoker... then it turned out my soul mate happens to be a smoker, so I learned to deal with it. I still don't enjoy it, I'd be overjoyed if he quit, if only for the few extra years it could buy us. If he smoked in the house, that would be a major problem, but he respects that I don't like smoking, and he takes it outside, even when it's -40. Also, he's a conservative, and I'm an NDP (the equivalent to, he's a republican and I'm a democrat). He likes S&M, me not so much, so he finds other women to spank on kijiji. These are some pretty "core" values for both of us, parts of our personal identities. But you mentioned compromise, and that's exactly what we do.
What I'm getting at is there are a lot of "values" I have that I used to think were deal-breakers, and it turns out that if the rest of the relationship is worth it, I can learn to deal with a lot of things.
I can click with lots of different people for lots of different reasons, and I can easily imagine meeting a girl who is my husband's polar opposite and having it work beautifully... I like to let relationships grow on their own, rather than trying to steer them in a specific direction. Usually my brain just makes things too complicated, but my heart is pretty good at knowing what to do.
I do not need a label to define me. Labels are sticky and I hate the glue they leave behind.