Australian magazine The Age tackles this question, summarizing a year-long study where several volunteers shaved their bellies in the name of science, to test the 'hair conveyor-belt theory.'

More incredible to me than the study itself, (which is insanely great research in the name of abstract knowledge) is the quote:

"Most people have belly-button lint and they want to know why it collects in the navel, what it is composed of and why it is almost always blue,"
-Dr Kruszelnicki

Wow. And I thought the blue-lint thing was just me. I've actually talked to friends about this. Nice to see I'm not alone!