I started programming in grade school. I didn't learn anything about algorithms until college. I don't think starting early helps out that much for anything beyond pretty simple concepts.
There are those who pick up amazing amounts, algorithms and all, on their own, but I think that has more to do with the person than with starting early.
I have the distinct memory of being in a college class with someone who had never used a CLI (no understanding of how to navigate from /home/foo to a project directory, only most tenuous understanding of what a directory was), who didn't understand what a variable was, and who couldn't understand why x = 7 + 2 when x already was 10. I have a lot of sympathy for folks who feel like the geeks-doing-this-since-age-7 have a pretty commanding advantage coming into CS101. (I just don't think that advantage is morally problematic.)
There are those who pick up amazing amounts, algorithms and all, on their own, but I think that has more to do with the person than with starting early.