I have over 15 years experience leading kids of all ages and I have to say in response to other answers-
Doing violence to your child in response to his violence teaches that violence is O.K. but only for people who are bigger and stronger. I certainly hope that you are not trying to teach that lesson (if you are don't bother reading the rest of this.)
Do not bite him, he is not capable of understanding the connection between his biting other kids and your biting him. If you bite him it is simply a violation of his inherent trust in you as his parent. The same goes for spanking, you only teach him that you can get away with doing violence and he can't.
In regards to actually doing something useful-
You need to find out what disciplinary procedures the kindergarten is using in response to this behavior. If they aren't doing anything and relying on you to solve the problem then they are not helping the situation.
The most important thing to do is make sure that he is clear about the connection between whatever actions you take and the actions he took (biting) that made those consequences necessary.
Make sure that you help him to remember exactly what happened when he bit the other kids and then help him imagine how he would feel if he was in the other kid's position. You do not need to actually demonstrate the violence, he is perfectly capable of imagining it, though he may need some help putting the story together.
Try to help him imagine a realistic scene to answer each of the following questions:
1. What would it feel like to be bitten by another kid?
2. Is hurting people a bad thing or a good thing?
3. How do you think your friend felt when you bit them?
4. Sometimes people lose control of themselves and do things that hurt their friends even if they didn't really mean to hurt them, what should be the consequence of hurting someone else?
I recommend that if you can help him imagine answers to each of the question then you ask him what he thinks an appropriate consequence should be for him when he bites other kids.
Ask him about his opinion of what they do as a consequence at kindergarten. Does he think they treat him fairly? If not, what would he prefer they do?
Think carefully about whatever he suggests as his punishment. Discuss what you think is reasonable and fair, then make a decision about what the consequences will be from then on.
Write down exactly what you decide is the appropriate consequences and have him "sign" that he agrees to it (even though he doesn't read or write this will make an impression that this is really important.) I do not recommend you invoke it for the offense that prompted the discussion unless he thinks that is fair. Making this big a deal out of it should have gotten his attention.
If he bites again then the consequences should occur as soon as possible and with only enough discussion to establish that he understands that he bit someone and therefore the consequences are exactly what you both discussed and wrote down. If he doesn't think it's fair anymore then AFTER the consequences have been completed you can re-negotiate the consequences.
The most important things are to make it clear that
1. he is not allowed to bite people,
2. your job as a parent is
a. to be compassionate for his struggle to master self-control, and
b. to enforce the consequences that you both think will encourage him to find a different way to express himself rather than biting.
If you find that you are still dealing with biting behaviors after administering a couple of consequences then focus on helping him discover how he is feeling just before he bites people and work on imagining different ways to express those feelings.
Good luck, below are resources that follow along the general lines that I have outlined. Don't be surprised if you have to take these steps over several days. Preventing this behavior is worth the investment of time at his age.
Adele Faber and Elaine Mazlish- Parenting Experts
Parenting with Love and Logic Site