We didn't advance him a grade- I think for many such kids, you trade the academic problems of not grade-skipping for the social problems of grade-skipping.
He is qualified for our full-time gifted program, which starts in 4th grade (he's in second grade). They keep talking about cutting it but hopefully they won't! Our older boy is in it now and it's grade-accelerated by a year. We just have him do little workbooks at home and he's happy with that. He's very social and sweet and he doesn't seem to care if he "learns" things in school that he already knew!