JOKER'S
SEXUALITY
The most common (and lesser known) sexual orientations I'll look at are: Heterosexual, Homosexual, Bisexual, Asexual, Autosexual, and Pansexual.
Hetero?
Sorry if you think that Harley Quinn is Joker's one true love and he wants her and only her and they were meant for each other. Joker is definately not a strictly heterosexual creature. Before the accident he was, when he was married to Jenny and they were having a kid together. But now? His homoerotic fascination with Batman aside, Joker has confirmed male lovers in his past.
I'll track down some images, but my favorite is in "The Devil's Advocate" when Batman is trying to track down Joker associates who may be carrying on his crime while he's in jail. Batman comes across one of his past boyfriends who says, "First he broke my heart, then he broke my legs." Come on, don't be surprised he's not hetero.

Lastly there is documented sex between Joker and females. You can sift through the mountain of Harley Quinn evidence, even from the cartoon. In "Beware the Creeper", Harley Quinn asks Joker seductively "Wanna try some of my pie? I'm sure you'll want seconds." And in "Mad Love" jumps up on the desk in lingerie and asks Joker if he wants to "rev up his Harley." It's heavily implied in the Harley Quinn graphic novel, but Poison Ivy's suggestion of Harley being drugged is equally convincing. Joker did try to kill her right after their "night." While I've yet to find really convincing evidence that Joker and Harley truly have a sexual relationship (I believe if only for the amount of time they spend together), in "It's Joker Time" #2, Joker seduces and has sex with a female producer of a talk show to gain privileges and to test if the security cameras are off. In the next issue, they talk about what foreplay they will use this time. Joker's not gay.
Other?
Well, we have documented encounters with males and females. The kneejerk reaction then is bisexual. Bisexual is a sexual attraction and orientation towards both males and females. In most cases if someone doesn't fall into hetero or homo, bi is the only other choice. But consider the lesser known orientations:
Is he solely pansexual? Is he also autosexual? What about Batsexual?
"Joker's Apprentice" spells out Joker's view of life to my satisfaction. He believes that only he and Batman matter. Everyone else in the world is just ways for Batman and himself to interact. Kill, save, avenge, torture, etc. If this is truly the case, then maybe Joker is only sexually attracted to Batman? While there's a lot of compelling evidence and Joker is most certainly in love with the Dark Knight, he is not only sexual attracted to Batman. He has relationships outside of the Dark Knight and his sexuality doesn't die with the Dark Knight. In "Going Sane" Joker believes he has killed Batman and returns to a sane, ordinary life, hooking up with a regular girl and falling in love. No, though it's been suggested, Joker's not a "Batsexual.
Is he pansexual? Is he autosexual? Maybe he's either, maybe he's both. Maybe he's just so bat-shit crazy that sex and watermelon have the same level of interest for him. Maybe his penchant for torture leads him to engage in sexual relationships just so it hurts more when he tells the person he doesn't care for them and is going to kill them.
In Christopher Sharrett's interview with Frank Miller (circa '91), Miller goes into some detail on the sexuality of both the Batman and the Joker. Describing the Joker's relationship w/Bruno in Dark Knight, he notes that the Joker "never had sex with her because sex is death to him. Put more accurately, death is sex." Therefore, the Joker seems to get some type of sexual gratification by causing mayhem and physical damage. If the violence against Barbara is put into this context, she was raped, minus the actual intercourse. Not that that's any better, mind you. On the other hand, if I put myself into the character of Jim Gordon and knew that the Joker had raped my daughter, I can see where the character would not be able to accept it and would focus only on the shooting (which itself is a symbolic raping with the phallic gun and penetrating bullet, and I don't think I have to explain the significance of Robin II being beaten to death with an iron pipe). Damn, maybe Wertham did have a point after all...