There are different kinds of rat bites.
Whoops, I thought you were food: Every once in awhile, you'll forget that rats are pretty close to blind, and you'll be feeding them some leftovers, and you'll stick your fingers in the cage to give some adorable rat-brain a scratch. Some rat, without fail, will think you've got more food because your fingers smell just right, and they'll try to grab it really fast. I don't know how they do it, but before puncturing the skin, they will stop, mid-nip, assess the situation, try to pull your finger in further, and decide that it's really not food after all. This bite really doesn't hurt at all, but you, as humans, have to train yourself not to flinch or snap your hand back, else it may lead to the second type of bite.
You startled me!: Sometimes rats are sleeping so soundly you think, just for a moment, that they're dead. Sometimes they don't look like they're sleeping quite that soundly but they are. Sometimes you'll give one of those rats a pat on the bum, and they'll whip around in a flash. If you don't get your hand out in time, you'll feel a little toothy pressure, and possibly a scratch or pin-hole. It's really best to wake them up by making some noise, in case you hadn't guessed, or make sure your hands are in plain view when you awake them. These bites tend to be disturbing at best, but really don't hurt all that much. Don't feel so self-assured though, because they really can cause damage.
Rats have two teeth on top, and two longer teeth on bottom. In rat school they were taught a really cool self-defense trick that we humans aren't capable of. They will separate their two bottom teeth which effectively enables them to get a better grip, and additionally, inflicts a nastier, more uneven, wound. I'm convinced they could hold onto something for days like this, though I plan not to give any rat the chance. Ever.
As a personal side-note, I've found that if you stick your fingers in the mouths of baby rats, when they get older, they are recognizably much nicer with your digits that those who did not have your fingers shoved in their mouths at an early age (see "How to avoid getting nipped - the terrifying test of will."). This will not prevent you from getting nipped if you startle one awake though.
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Disclaimer: There are many non-sarcastic accounts and tips on the web regarding rat care. This is not
one of them. These are merely accounts of our experiences with rats, our perceptions of these experiences, where we've failed
and where we've succeeded. These accounts are here for two purposes: