I read an article on CNN.com this morning about the last interview Evel Knievel gave (it was with Maxim). In it, he discussed how he found God in a hotel in Daytona Beach after being an atheist for 68 years. Unfortunately, he did not take it upon himself to tell us which room in which hotel so that we could all go and visit God, but, oh well, I am sure that someone will run across him again eventually.
How deathbed conversion (he was not on his deathbed at the time, but had been diagnosed with a rare lung disease with no cure) has been portrayed doesn't sit well with me. This is mainly because the cause of it never is clear, however, everyone assumes it is because God came to save them or because they believed the whole time but didn't admit it. I see a few reasons one would convert on their deathbed.
(1) Their illness is causing them to hallucinate God, Jesus, angels, loved ones, etc. and provides them with the proof they needed to believe in God. There are a lot of stories of people experiencing this the days before their death. My grandmother, for one, had a long conversation with her deceased ex-husband in front of my dad and I. Seeing God, Jesus, or angels can be a pretty convincing argument to anyone if in the right state of mind. As for seeing loved ones, it would be possible for them to feel like they were crossing over into the afterlife during these moments.
(2) They succumb to the popular Christian comeback of "What if you are wrong? It wouldn't hurt you to try it just in case." I would think this would occur more often with people who have not yet come to terms or made peace with their own death. It may be more of a last minute grasp for life, not an actual change in beliefs.
(3) They want to put their loved ones at ease. Most of us are not fortunate to have all of our loved ones agree with our beliefs and we understand that, to them, it means that their son, daughter, sister, brother, etc. is going to hell and they will not be able to see them in the afterlife. Some non-believers may choose to take that step at the last moments so their loved ones can be at peace with the imminent death.
I think it would be impossible for us to say whether we would or would not do any of these during our last moments. Illness and fear could take over in ways we never prepared ourselves for, but if I ever do, hopefully it will be because of 1 or 3. I like the idea of being able to talk to someone that I love and haven't seen or spoken to in a while in my last moments and I don't see it as 100% bad to give a gift in the form of comfort to those I hold dear.