An off-spec is any talent distrubution that doesn't agree with a class's canonical raid role. Shadow Priest, feral or balance Druid, retribution or protection Paladin, elemental or enhancement Shaman, or fury or arms Warrior. You'll notice that those are all classes that can heal. DPS classes don't tend to have on- vs. off-specs per se, since by and large all of a DPS class's talent trees add to their DPS. Their raid role is to DPS; therefore, all specs help their raid role. But for a class that can heal, most of the time, their raid role is to heal.
Now don't get me wrong -- I'm a huge supporter of raiding shadow Priests, feral Druids, and all the rest. Your character is your own, and you should spec it however makes you happy. With that in mind, what's your favorite off-spec, either to play yourself or to have in your parties/raids?