I don't think it's as clear-cut as "drunk people can't consent". Being drunk doesn't make you a child or a completely different person. Are you perhaps impaired if you drink enough ? Sure. But unless your drink was spiked or you were manipulated or coerced, you took a calculated risk and are responsible for your own freely-made choices.
If you killed someone while drunk - you're still responsible. Being drunk doesn't take away responsibility for your own actions.
There are certainly different levels of "drunk". You can be drunk and physically a little wobbly but have no mental impairment - thus being able to consent in the fullest sense of the word.
Drunk people still have the same right as anyone to say "no", and it should be respected just like anyone else. And, duh, no - you should never have sex with someone who is passed out or who is so drunk that they literally don't know what you're saying and can't respond one way or another (that would be a great time to get someone to the hospital, instead).
I've had sex while slightly drunk. We talked about it beforehand - and even before drinking. It wasn't that great, but o well.