Well, I've done things for jokes a few times. In one case it was for lack of a better term, an asexual aristocratic (as in, he took a level in the class) male bard, both he and his "dear friend" (another aristocrat played by my friend) extremely androgynous and wearing only the finest garments and perfumes. In this case, they had no particular interest in anyone and were just complete narciscists, but their appearance and extremely cordial relations with one another could easily lead one to think otherwise...
Another time, I had an ambiguous gender bisexual Changeling rogue warshaper in a party with a complete and utter boor of a character, that proudly roleplayed his abysmal charisma score appropriately, being a jerk to everyone. He also liked to hit on women and made it pretty clear he wasn't above taking advantage of one that was drunk or otherwise not in her normal senses. My character took it upon itself to make sure the cretin could never breed / pass on his bastardy genes, and spent its spare time in the guise of women for him to "charm" only to later in private squick the hell out of him by sprouting a tentacle out of the mouth or some other body horror, the ultimate goal being to forever mentally scar the character from attempting to sleep with anyone. Played for laughs, of course.
On a more serious note, one of the characters I'm currently playing is techincally a hetero male, but both he and his NPC significant other have kinky imaginations and the ability to polymorph into various genders and creature types, and I've made it pretty clear that, within the confines of their monogamous relationship, he's open to pretty much
anything. It's mostly left offscreen, aside from occasionally squicking out the other PCs with his bondage-themed spell selection, including Evan's Spiked Tentacles of Forced Intrusion (thank you for the inspiration, OotS!).
Another character I'm currently playing is another Changeling (I like 'em). Definitively a male, but his whole thing is that racial and gender lines are meaningless and not worth all the fuss people make of them, all that matters is distinguishing yourself in this life. To this end, he changes his gender and race as often as he wishes to match what he is currently "feeling like," but doesn't use it for subterfuge, just a visual manifestation of his self. In accordance with his outlook, he is "bisexual," you could say. It's again, pretty much left in the background, though, not a major source of internal conflict.
In general I'm very open to playing different genders and sexualities, but I don't really define my character by it that much, and I mostly game for light haerted enjoyment, not drama. When there is drama and it's not the "super villain has your family member hostage" variety, I prefer it to be on philosophical / metaphysical grounds, not romantic.
EDIT: I did once have a female druid become romantically involved with another player's male monk PC, as they were long lost friends, but the courtship mostly involved heavy flirting on her part and didn't get too in depth on screen.