On a slightly different note, is it common to take a year off between graduating and starting residency?
Is it common? Definitely not. It's actually generally frowned upon in certain specialties.
The logistics of applying for the Match while not an MS4 or a current resident can be quite difficult. Your LORs are going to be a bit out of date, you'll have to be in frequent contact with your dean and registrar, etc.
Plus, people will think that the year off will have dulled your clinical skills. Not to mention that you better have a REALLY compelling reason for taking a year off after MS4....
(EDIT: This doesn't include, for instance, spending a year providing basic medical care to villagers in Laos, for instance. That would actually be a good thing to talk about to residency interviews, and it still keeps you clinically involved. Pregnancy, taking care of a sick spouse/parent, etc. are also good reasons. However, taking a year off to backpack through Mexico and drink a lot of beer is NOT a compelling reason.)
plenty of people who don't match end up doing this. they take a year to do research or something else and beef up their resume to reapply for the next year.
I wouldn't say "plenty." It's actually fairly uncommon (although not THAT uncommon) to do a research year after not matching. It depends on which specialty you were originally applying for, and how much you'd like to re-apply in that particular specialty the next year.
If you do something like ortho or integrated plastics (i.e. very competitive), and want to re-apply for that field, then doing a research year probably makes a fair amount of sense. It shows that you're dedicated to that specialty, and don't want to entertain any other fields.
Otherwise, if you don't match, it's generally recommended that you do a prelim year, in surgery or medicine. It proves that, while you weren't able to match the first time around, you WERE in fact a good intern, it will get you updated LORs, and may allow you to re-enter another categorical program at that hospital.