I always refrigerate unwashed, and when using, take them straight out of the fridge, and crack them. Haven't had any issues.
Only time I wash eggs are 1) if one is pretty filthy (but not so bad that I wouldn't eat it or 2) I'm going to soft/hard boil, which is just my personal quirk. Obviously the boiling water would kill any bacteria, but I can't get over thinking about the eggs bobbing around with boiled dirt, so I scrub and rinse beforehand.
