The kind of evidence would depend upon the kind of afterlife. One notion of an afterlife that ought to get at least a little respect around here is this:
However, whatever "near death experiences" really are, they are not evidence for an afterlife as speculatively described here. Information about Omega's activities doesn't flow into our naturalistic universe. Instead, information about our universe flows out. The kind of afterlife I have described leaves no evidence.
So, what kind of afterlife does leave evidence? I find it hard to imagine an afterlife scenario in which the Omega in question is so sloppy as to allow information to leak back into his simulation.
ETA: Hmmm. Now that I think about it, my speculation described two universes - a completely naturalistic 'first-life' universe, and a less naturalistic 'after-life' universe. Information clearly does flow into the after-life universe. The origin of each reincarnated mind requires a miracle. So, I guess what I am saying is that I doubt the existence of evidence that there will be an afterlife. But I suspect that evidence for an prior life should be pretty overwhelming once you get to the afterlife. So, I'm pretty much ruling out Hinduism - at least as I understand it.
I was on Reddit today, and I came across (this link)[http://www.reddit.com/r/AskReddit/comments/eyiat/for_those_of_you_who_have_died_and_been/]. One of the things I've seen on this site that's bothered me is the exclusion of personal experiences in deciding what a person should or should not believe. I know that less wrong is mostly atheist, and I wanted to hear less wrong's reaction to descriptions of experiences like these.
For example, my dad was in the hospital 5 or 6 years ago when a truck came across an icy road and hit him head-on. His most vivid memory from this is a dream he had when he was in the hospital. He was in a pool of water with my mom, and they were both naked (they were underwater, but didn't need to breathe). He remembers that at the end of this pool, there was a bright light that he wanted to head towards. He began to swim that way...and here, I don't remember what happened, but he was unable to reach the light for some reason.
Such stories seem to be common for people who come close to death, and for a community based around rationality which seems to consider the likelihood of life after death as slim, I just wondered what your reactions are. My reaction is that such experiences are explainable in terms of neural activity, but that doesn't necessarily exclude the possibility that these are descriptions of experiences of an afterlife. I'm not convinced by them, but I do consider it to be possible.