TarSnap and Pinboard are my favourite examples of businesses that don't need VC to succeed.
There are lots of bigger ones, like imgur, Github, Atlassian (I think), 37signals, Fog Creek, etc.
Pretty sure Fog Creek has never raised either, while having 50-100 employees.
The overall point is that you don't have to be a one-person business to grow at a slower but "healthy" rate.