As someone who has long been both contemplative on the concept of theism and religion and inquisitive as to the rationale others have for ascribing to them, I've naturally reached some conclusions over time.

The main conclusion to note is the ultimate reason for belief that you'll get from the religious if you stick to a discussion with them long enough:
1. They insist on a logical fallacy or reject science outright
2. Personal experience
3. None whatsoever (just faith)

The first are the fundamentalists that even a large number of religious call crazy.  So let's discount the blatantly stupid and address the two main points, faith and personal experience.

Providing absolutely no reason for believing something means you will accept anything that feels good, really.  Given faith is by definition unreasonable, I think you'll forgive me for discounting this one as well, for lack of a better term, rationale as well.  This is actually rarer than the last one, which is personal experience.

Finally to the point of this post, personal experience.  Many will claim to have had a personal experience that affirms their relgious beliefs.  Certainly noone can tell them they're wrong just from that statement, because nobody else has had that personal experience.  It's completely unique to the person and they may in fact be completely justified.

However, even ignoring the possible interpretative complications of attributing the experience to a god and not something neurological, there's one question unanswered that I think is a perfect example of the kind of thing that gets atheists annoyed at the beliefs and attitudes of the religious, even if it's not at all meant to be negative or insulting.  I am referring to a personal sense of superiority and entitlement.

When you tell an atheist that you believe because of a personal experience, you are directly stating to that person that you believe he is not good enough to have a personal experience with that god or too stupid to recognize one.  If you're a Christian saying this, you're implying you're more worthy than the Buddhists in East Asia, the Jewish who still do not accept Jesus as the savior, the tribes in remote regions who have no exposure to your religion.  Worse yet it is if you believe in the concept of a hell or afterlife punishment such as reincarnation to a lesser being, that just because the billions others who never got this revelation should have to suffer for something they had no basis to believe.

Even just theism, a belief in a god, but not necessarily one of an existing religion, you're still essentially annointing yourself, perhaps even moreso.  That this revelation be so incredibly unique and special that so few have had the honour such that the religion dedicated to that god doesn't even exist.

If personal experience if all you've got, then come right out and say it: You were chosen by God Himself.  If you think that's ridiculous or pompous, maybe you should think about that.