I find it difficult to imagine doing extensive web work (Rails, Django, PHP, JS) without ever touching GitHub.
Surely, in the course of your daily work using giant open source projects you'll file a bug, comment on an issue or even submit a pull request. Most large applications are built off of dozens, or hundreds, of open source libraries—all of which have bugs at various times.
I don't expect all web developers to have side-projects or libraries, but I would expect they'll interact with open source projects in some way. This way of thinking clearly doesn't apply in more closed source worlds like games, finance or giant enterprise—but it certainly holds for startup/web work in my experience.