You know, if someone were to ask me which trait is more important in deciding whether to get into a relationship with a girl - looks or character - i'd say that it really depends.
People normally say that looks are only skin-deep and would fade with age. Thus character is always the more important trait. However - and this surprises me too - i think i disagree with that analysis to an extent. Because i think that, while looks fade with age, character can also change before and after a person gets into a relationship. A person who seems quite nice and alright could be selfish and bad-tempered towards his/her family and therefore towards the people he/she becomes close to as well. Or someone who seems mature and emotionally independent could become the exact opposite (e.g. possessive and demanding) after getting attached.
So if you're patient enough to find out about the guy's/girl's family relationship and become a really close friend of that guy/girl first before making a decision as to whether you truly want to spend the rest of your life with that guy/girl, then go for character. If you don't have the luxury of waiting around, then looks might be a better choice to ensure at least a measure of satisfaction afterwards and lowers the risk of a breakup after a long, long courtship.
Of course, there are exceptions. First, lots of makeup, wigs, things that make you look far better than you normally do, etc. 'Nuff said. Secondly, i think you can probably tell immediately if a handsome guy/beautiful girl is nevertheless a psycho, or - if the character incompatibilities are less obvious - you might still be able to notice warning signs if you're perceptive enough.
Most importantly, however, even if you go for looks, i think every relationship needs a bit of give and take to sustain it. A bit of sacrifice from either party, for the other party, so as to create a feeling of indebtedness. Now, people might call me unromantic or calculative, but i really do acknowledge the power of indebtedness in all relationships, even in romantic relationships and familial ones. At the very least, it is something tangible that we can hold on to.
So, my advice to anyone in a relationship right now is to constantly look at yourself, see if you are pulling sufficient weight in your relationship, and try to give as much (or perhaps more) to the other party as he/she is giving to you, whether it is physical assistance, or material or emotional support. If you don't feel any sense of indebtedness, then maybe you're not sufficiently acknowledging the things he/she does for you...or maybe the other party's an ass. But of course, the key in this exercise is to generally be more patient with the other party but more demanding with yourself.
Certain (mostly familial) relationships can survive even with one-sided sacrifice, but if people on both sides of relationships constantly look at themselves and review themselves (especially for the important relationships), i'm sure there will be longer and happier relationships all around, romantic or not.