Who started it: Jay-Z
Circa: 2003 

When Jay-Z dropped The Black Album in 2003, he was preparing to transition from rapper to "business, man." As such, he eschewed sports jerseys and T-shirts for a more grown-up look. But he still kept his street cred intact by throwing a fitted on top. The resulting look from the "Change Clothes" music video caught on, and became a de facto uniform for dudes who wanted to be able to get in the club without looking like they just got off work.