Wow...this is a surprising thread.
Yes residents do get vacation. All programs give vacation, but the time varies - and it's very program specific. Most places give 3 weeks of vacation, and a great many give an additional week of time over the holidays, depending on the field, coverage required, etc.
Most places will place restrictions on when you can take vacation as well. There will be certain rotations that are "mission critical" and have to be staffed. As a pediatrics resident, for me, this includes any wards month, NICU, PICU and ER months. My vacations are limited to being taken in months where I'm in outpatient clinics or electives, where they can afford to not have resident staffing. Because I get my schedule of rotations a year at a time (ie in May 2010, I knew what rotation I was going to be on in June 2011 at the end of my 2nd year), I had to request that certain months be reserved for vacation worthy electives. And at least in my program, I'm not allowed to take more than one week of vacation in a block. If I wanted a two week holiday, it would have to be two vacation eligible months back to back connecting the last week of month 1 with the first week of month 2.
The other key point in most programs is that you can't separate out vacation days. You take a week off en bloc. No snagging a vacation day for a long weekend here or there.
Some programs will be more rigid, some more flexible. Some less generous, others more. It's certainly one thing to consider when you begin looking at residency programs during match.