My son (just turned 5) was like that, and he eventually grew out of it.
We took a couple different approaches. On the punishment side, we'd go with time-out, or isolation in his room; we felt that giving him a lot of interaction for his bad behavior would just be rewarding it. (He has two older sisters, so it didn't particularly surprise us that he would decide that "bad attention is better than no attention.")
On the training side, we would teach him some alternative behaviors, like blowing instead of biting. To be honest, other people found the blowing bothersome too, but in our view it was miles better than biting.
In general we found that if we gave him a ton of attention, that would keep his behavior good, but of course sometimes (especially with the other kids) that just isn't possible.
If the behavior lasts into preschool (it did for us), it will cause problems with the other kids, teachers and parents. You will want to pick the school carefully.