From a female's perspective, these are the important things. They are important to both parties in the relationship.
Communication: Nothing will get accomplished if neither of us knows what the other is going through or feeling. Very quickly you end up alienating each other. Talk. Even if you're not sure what's up just yet. Tell her what you do know. When you get in an argument, remember that you love one another and don't do anything to overtly hurt the other. Sometimes it's too easy in the heat of the moment to shove in that little dig that will put a fracture on the relationship. These are more difficult to heal than they're worth. You're in this together. When your communication fails, your relationship will be shortly behind it.
Honesty: If something happens, let her know. Don't lie to her. This goes both ways. It's extremely important to remember that your partner has the right to know the truth. Many times, a lie will come back to bite you in the ass. Most people aren't very good at covering them up for extended periods of time. Give her information that's important when you have it, not when it's about to become relevant to the situation at hand.
Equality: The rules must be the same for both of you. In my relationship (which is odd and open), it's important that both people know where the boundaries are and that the relationship, in this way, are equal. If you're allowed to go out with your buddies, she should be able to. If she's allowed to buy toys and such, you should be able to. The second the rules are vastly different for both parties, resentment has the chance of sneaking in, particularly if it's something the other person wants but can't have because of the differences in expectations. This also includes housework. If you both work the same amount, the housework should be divided somewhat evenly.
Consistency: If you say you're going to do something, try to make sure it gets done. Many times, I've seen fights happen because someone didn't do something they said they were going to do, or they've started back up on something they said they wouldn't do. Don't look for a loophole. This is almost an extension of honesty, but can often just be behavioral. It's important to remember that you depend on your partner's word. If you can't rely on them for basic things, the relationship can quickly become unstable.
Romance: If you didn't want to have sex, you would have just gotten a roommate. They're less maintenance in the long run. But, that said, you both need to take steps to ensure that your sex life stays alive. Don't lose the touch you had when you were dating. It'll take more work to get there, but the care, commitment, and romance is much more satisfying. Try new things. Have nice evenings out. Surprise her with a romantic outing (or perhaps something more intimate in your house). Much of the time, when a woman feels sexy and loved, she'll go out of her way to be sexy for you. It sounds a little silly, but it's a concept that needs to be reinforced. Let her know that she's sexy (in whatever way you two have worked out).
Did I mention communication? I can't stress how important it is to talk.
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Did I mention communication? I can't stress how important it is to talk.