Apparently, last year Minnesota passed a law making it mandatory for parents' health insurance to cover their (unmarried) kids up until age 25. Thus, as far as I can tell, I'm not uninsured! Hooray!
If you're not from MN and don't have a job with benefits yet (?), it's worth checking to see if your state has a similar law. I saw that Utah has you covered until age 26...there's probably others.