There are usually wrongful death and damage to property lawsuits filed against the airline after every accident. These happen regardless of who is at fault (both UA and AA were sued for the 9/11 incident, for example). Most of these are settled by the airline's insurance company. I guess one could theoretically sue the pilot as well, but the airline has more money (I'm not being facetious, that's how lawyers think).
With regard to criminal liability, it would apply only in case of negligence. Think about driving: getting into an accident is not a crime, even if it was your fault because you weren't paying attention. But if you were violating a specific rule (driving while intoxicated, talking on the phone, etc.) then that is a criminal matter.
Here is ALPA's take:
http://www.alpa.org/portals/alpa/mag...lLiability.htm