1) Keep everything in front of you. If you are running man across the board and bringing extra rushers (or doubling some people) and a swing pass, or run play gets to the second level, you're looking at a big gash in yardage (possibly score).
2) Zone provides a base that's easy to get back to when things are going wrong. Carl Banks remarked one of Sheridan's problems was that when our defense was being abused over and over, we wouldn't get into a base zone as a "reset". We kept reacting to the last play instead of preparing for the current one.
3) Zone follows the philosophy of providing "traffic". Most of your picks are in a zone defense when a QB doesn't see someone playing center field.
4) Zone also follows the philosophy of assigning players "permanent" positions from which you can then add your wrinkles in. In other words, when asked to blitz, you know who/where your back up is.
Generally speaking, when you bring an extra man (or more) on a blitz, your zone becomes too open (not enough coverage) so you go to man coverage to make up the difference. Often you will see a combination of zone and man coverage on almost every defensive play in the NFL. The caveat here is the sell out blitz (when you bring two or more extra rushers) and the zone blitz (where you bring an extra rusher (Safety or LB) and drop a dlineman).
We ran pure zone about 40%(ish) of the time in 2012. When we've done this, its almost always been in a Cover 3 look. Normally we run a Cover 2 shell with single or double man underneath (although our Safeties tend to cheat a lot on that). Very occasionally we've run pure man coverage (we almost never blitz that many players).
We ran a type of zone about 90%+ of our defensive snaps this year.
Hope that helped