I'm fairly open when it comes to relationships, but there are a few things I consider paramount.
Heavy bonding - If there's one thing I can't stand, it's aloofness within a relationship. If I'm in a relationship with someone, I'm pretty much saying "I really think I want to marry/be with you". Casual dating doesn't exist in my world lol. One of the #1 things I look for is that same "serious commitment" in a potential partner (I'm bisexual).
Intrigue - Often times, I know at least 5 times more information about my gf/bf than they know about me. It's not that I'm not comfortable sharing or whatever...they just don't ask =/. And when they do actually ask, they tire quickly. With friends, it doesn't matter as much. I VACUUM in information about them, and they learn about me over time. That doesn't really bug me. But if I'm thinking about/actively dating "you", one of the biggest turn-offs for me is having the person not be interested in me.
The Geek Factor - If you were to look inside my mind, you would see passion on all sorts of subjects that most people either find boring, or pointless. Modern Neanderthal theory, nature and/or nuture in relation to homosexuality, a BONFIRE of passion when it comes to world religions (ex-Christian), etc. When I talk about my theories to most people, they just nod, say "uhhuh", and then move on to another topic. This is JUST as annoying as a lack of "Intrigue". I'm not saying that s/he has to have all of my same interests, but it would be nice to have him/her at least acknowledge my perspective as interesting =/.
"Sexual openness" - This isn't quite what you think it might be. I don't mean "does x, y, and z a LOT". It's more about an overall outlook on sexuality at large. For instance, I'm what you would call pro-polyfidelity. Polyfidelity is basically non-religious "polygamy/group marriage". But it's not just 1 man, many women. It could be 1 man 2 women, 3 women 2 men, 1 woman 3 men, etc. That's what I mean by sexual-openness. Even if I end up marrying just a single girl/woman (which I probably will..that, or I'll be her long-term bf), being open to it is the key. It shows how the person thinks, how willing to be different they are, etc. THAT, right there, is gold to me.
That's pretty much it. At least, the things that aren't "personal" lol. To be honest though, I wouldn't mind talking about them. I'm just not sure if the people here would mind =/.