I think a woobie does need to be both kickass and damaged. It's the conflicted nature that sells it. The fact that they need a hug so badly but would never deign to ask for one.
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I also think Destruction is woobie-esque, as is Delirium. I could be over-woobiefying, though. Or perhaps The Endless lend themselves to woobieness.
Hmmm. I don't get a sense of woobieness from Destruction or Delirium. Del has Barnabas to keep an eye on her, and Destruction ... I just don't see him needing a hug, a blanky, and some hot soup. Or someone petting his head.
Morpheus has the emotionally-crippled-and-needs-a-hug-and-a-bowl-of-soup thing down cold, but when I think "woobie," I think of someone who needs protecting from the harsh uncaring world, not from his own choices.
But he makes those choices 'cos he doesn't quite understand the world around him, poor baby.
I sense another round of re-reading Sandman in my future. Oh darn.
Well, maybe if you interpret "cuddle" as "athletic sex."
I'm good with that. The "[Male Character X] is a woobie that needs teh healing sex" subculture could use a female version.
Hey, Broomy, you should buy me all of Sandman for my birthday. I'm just saying.
Maybe it's a term that can only apply to people that try to give off an image of strong or scary, but don't back it up and make you want to hug them anyway.
Batgirl could fit that, I'd imagine. So could Aeryn, perhaps (haven't watched, am speculating, don't shoot me.) Buffy, even, perhaps, only I don't think she generally does, or Willow-trying-to-kill-Glory, maybe. Maybe it happens in Dark Angel at some point, if they ever develop characters beyond hot boy and hot girl. Might could happen with Rebecca in The Inside, too. I think Clarice Starling has it a bit.
Faith?
CRYING CHRISTIAN TROY.
Faith in the alley at the end of "Five by Five," maybe.
For the sake of procrastination (ye gods, I do NOT want to be at work today!), the Endless from least to most Wooberific:
Death, Desire, Destiny, Destruction, Delerium, Dream, Despair.
[edited to show that I know the difference between least and most]
people that try to give off an image of strong or scary, but don't back it up and make you want to hug them anyway
See, Cass is strong and scary. She can beat Batman in hand to hand combat. The implication, however, that she's emotionally strong (as opposed to precisely cauterised) that one may draw from her physical capability is where the woobie comes in. She's a lost little girl who can beat the world's best non-meta assassin.