Well, since you asked

....
My current character started as a dwarven druid who was spurred into adventure by a series of prophetic dreams, in which he met his death at the hands of an elvish woman.
Well. He reached seventh level before meeting his death at the hands of a nasty destrachan. My friends recovered his body and took him to a friendly druid NPC for reincarnation.
My DM didn't want to roll for reincarnation, since that's such a crapshoot -- he wanted it to be story-based. And he took my suggestion:
I'd misinterpreted my dreams. That elvish woman wasn't my killer -- she was me.
So now I'm playing an elvish woman with the soul of a dwarvish man. She's not entirely sure how to deal with it, expects the Goddess she worships is having a joke at her expense.
The other party members are a male lothario (played by a woman) and a male Cha 7 elf (played by a man). The lothario never knew my PC when he/she was a dwarf, and he hits on the elvish woman occasionally; my PC snarlingly rebuffs all advances.
OTOH, the elvish man has been her only constant traveling companion since the campaign's beginning, and despite his unkempt unfriendly self, they're awful close....
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So that's my character. In the game I run, I've suggested the group call themselves the Jittery Trannies, due to the prodigious quantities of coffee the PCs drink and the ubiquitous genderbending. The PCs include:
-a female elvish fire wizard, played by a male.
-a female half-orc battle cleric, played by a male.
-and a male fighter who used to be female until she was betrayed by a djinn ally and turned into a male, played by female.
Victor/Victoria, anyone? Glen or Glenda? It gets confusing

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Nonetheless, the group is very responsible about all this genderbending. We play a relatively sexless game, but we'd probably do that no matter what sexes we played.
Finally, are you wondering what sort of character type you couldn't play as either sex?
Simple. One of the starting characters IMC was a teenaged mom with a six-month-old child.
Daniel