Any thing with a mouth can BITE!!
And after having my hand attacked by an over zealous clown fish I can tell you it's true. Now what you really need to ask is how likely is it to bite. The answer to that depends on the animal and its personality. I try to get to know the animals we have so when people ask me I can give the most honest answer I can. They all seem to have their little quarks. For example I would say a Guinea Pig is the least like pet to bite BUT... we had one that was the meanest little bugger around. When I would reach into his cage to get the food bowl he would charge at me teeth bared and ready to try and take a chunk out of my hand. This was not a piggy I would sell to someone with little children despite piggies being one of the best choices for little ones.
Even pets that you have had for a while can bite you. If a sudden noise scares your pet it might react by biting we see such incidents every year with dogs who are afraid of fire works. If a pet is ill it might also react to handling by biting they simple have no other way to communicate.
I feel this is something we as pet lovers need to understand and something we need to be aware of when choosing a new friend and companion. Nothing will spoil a little ones love of animals faster then a bitten finger. (and yes I know there are worse thing that can happen when a pet bites)