I haven't bothered to weigh in on the whole Btooom thing. Largely because it's off-topic, but mostly 'cause I'm lazy. Zach's rape stuff is kind of interesting though, and it relates to why Btooom is a bad show (shut up, it is).
Hmm rape scenes should not be shunned from anime or any medium. It can be a very powerful tool towards plot and characterisation, especially in drama, detective, slice of (real but fucked up) life and so on. It is all about how it is represented; it should be shown as a very mature theme, rather than something that is not explored by the show, trivialised, ignored and what have you.
Examples of good rape (hahahaha that sounds so so sooooo horrible) scenes; in Kite, Perfect Blue, kind of creepy semi rapey scene in Paprika, Berserk (that scene is not a 'close upy' as Kite but so much worse), not as much seeing rape but exploring the issue in EF: A Tale of Melodies, similar thing is done in Now and Then, Here and There (and better done then Ef I reckon)....ahh! Elfen Lied... hmmm that is all that comes to mind at the moment.
It is not so much wanting to see rape but, wanting to see rape used correctly in a series. I enjoy rape scenes.... When they move me to tears, and I start yelling how unfair it is. Or they make me disgusted at the reality of life, the nature of some people, when it makes me yell in rage, thrash about on my couch in frustration... when it is emotive and meaningful.
I certainly do not enjoy rape scenes because they what they are, scenes of rape. That is fucked up and as Hark0n said, there is hentai for that.
I do not remember any rape scenes in Accel World but, that crazy clothes stealing pumpkin head dude at the beginning kind of alluded to the abuse possible in the virtual world. I can imagine it would still be pretty trumatic if your avatar was raped... and you cannot log out.
Zach, I think you're right that rape can be a powerful dramatic tool, but I think that's kind of half the problem. It's just too easy. It's an out for bad writers, like gore and psychopaths (hey, look at that, Btooom has all of those things). Can't think of a good way to up the stakes, or give your (almost always female) character a traumatic back-story? Easy! Just use rape. It's cheap, and exploitative, and after you've seen it a few times it becomes incredibly boring as well.
To be fair, Zach, all the examples you mentioned were good ones, or at least not offensive or exploitative. I feel there should be a Godwin's law for rape in fiction though, because more often than not its presence marks the point where it's safe to drop a series.
To make it even more offensive in Btooom, Himiko goes on to be the very image of the afraid-of-men, feminist nazi so commonly used to brush off feminism as extremist and born of irrationality and trauma, only to then go all deredere after the lead saves her useless ass a bunch of times. The fact that the series makes her practically 100% burden doesn't help either.
The extreme male gaze during the scenes doesn't really help either. But hey, at least it's a better take on game-turned-reality than SAO.