What would make you convert to a religion?

Now here's an interesting question.

Especially if you already subscribe to one religion, what are the sorts of things that another religion might profess that would make you want to convert to it?

Would miracles be part of it?
A moral code?
A set of laws for governing societal behaviour?
A 'better' deity? (And what would make one deity better than another?)

Equally, are there any religions could you adopt that would not require you to renounce your current one?

Are there any that would mean that, if you did not already profess a religious belief, you would not have to change any of your ideological outlooks? i.e. are there any religions around that would not require you to change your mind about some currently held idea or ideal? (Perhaps with the exclusion of the fact that a deity actually exists!)