D.K.
J. -
my son did the same thing at 18 months. It didn't last long - maybe a few months - but it was a difficult thing to deal with. And embarrassing!
We just would steer him away from people that he wanted to bite. We would pull him away, we did anything to distract him and constantly told him that we don't bite other people.
I tried NOT to always say NO! because the more my son heard it, the more he tuned it out. I used other words and gave him objects to bite into (teething toys, soft toys) instead.
Some mothers told me to bite my son back when he would bite. But I never agreed with this idea. Since he's hurting others, I should hurt HIM to get him to stop hurting? It didn't make sense to me.
Realize that in a few months, it will stop. It's just very frustrating for now.
Good luck!
PS - in response to Beth's answer - my son didn't bite out of frustration. He bit because he could. It was something new for him and he joyfully did it to others, especially at play groups. I can totally see frustration playing a part with some kids - but it wasn't applicable with our son. Ahh, the joys of childhood! :o)