A lot depends on the age of your child, the temperament of your child, and the type, and length of camp. Also, are there camps geared toward their specific interests? I wouldn't send a child to camp just to "socialize" them, or get them out of my hair. Colleges often offer camps for older children, and some may also include college credit, and scholarships.
if there is a local day camp available, see if you can observe and evaluate their program ahead of time or find families who've sent their kids. If they don't have a fully-rounded activity schedule and a lot of free time without a lot of manipulatives and creative play materials, plans for foul weather activities, etc., I wouldn't be that keen on sending my child there. I wouldn't feel comfortable sending a child to an overnight camp until about 4th grade.
I had a sorry experience at a local day camp with my then (very introverted) 6 year old, discovering that rain cancellation of the outdoor activities meant the kids played board games all afternoon, and he just sat by himself at a table. After that, I felt my own programming at home was a great deal better. The same child, older, didn't care for our outdoor summer church camp either. When he went to high school, and discovered a science camp at a college near us, he was very excited, enjoyed it, and has returned every year. He is one who does make good creative use of free time, however, and has good self-discipline.
My younger son started to go to that same week long church camp every summer, and loves it! He's also involved in a week long music camp, and is attending the same science camp as his older brother this year.
It's definitely not a "one-size-fits all" scenario.
And we're looking forward to going to Science camp seminars tomorrow to see our sons' presentations of their projects and research, and HAVE enjoyed a few days to ourselves for a change!