i think it's a matter of how much you owe, and how quickly you want to start paying it back. i know many residents that opted to stay on as hospitalists as above. i also know quite a few that took a research year or two. i personally went straight into a fellowship, but it's an atypical one -- i get paid to get my mph.
my friends who opted to go into the workforce took varying amounts of time off -- some waited 2 or 3 months, others took longer than that.
most fellowships, however, would like you to start on July 1. a couple will let you start off cycle, but it's probably something you have to negotiate when you interview.
some fellowships can be worse than residency, however, if it's an acgme-accredited fellowship then they have to follow the work hour and other acgme restrictions.