The short answer is yes they can and do spin.
There have been several instances where airliners have entered spins. Airlines use the terminology "upset". Quite a number of airlines have been "upset" at cruise altitude. The first thing to happen is the autopilot disengages and sets off an alarm. If the nose is not immediately pushed down, the airliner will usually drop a wing and either flip over on its back then enter a aggravated spiraling dive - a spin or directly enter the spin. At this point the airliner is more in danger of coming apart due to over speed than uncontrollable.
There are a few minor differences with the characteristics of swept wing aircraft. There is a tendency for swept wing airplanes to have a lower nose done attitude then conventional aircraft - causing more of a spiraling dive (this happened in the Colgan accident). However the F-104 (Bob Hover had to eject) and the F-14 Tomcat, are well documented to enter unrecoverable flat spins.
One early Boeing (I think it was a 727 in the late 60's) flew better after the "upset" then before. Boeing spent a lot of time studying it but never figured out what happened. It is believed something was bent in such a way as to improved the flight characteristics!
In order to recover, several airline pilots have deployed the gear and/or spoilers. Several of the aircraft that lived to tell the story have had pieces of tail, gear, spoilers, engine cowls, wing tips, wing parts - ailerons, or fuselage separate from the aircraft. There have been at least two accounts where the wings were bent!
The last account I remember is a Japanese B-747 airliner about 4 years ago "upset" from the autopilot being disengaged. The pilot denied disengaging but they think he may have been playing around. It entered a spin (almost completely flipping on it's back) and he extended the gear. Gear doors, metal and parts near the gear wells came off, part of the tail also separated from the aircraft.
The long answer is yes airliners can and do spin, but survive-ability is marginal.