I would never fly AirTran (formerly ValueJet) for safety reasons. I would also never fly Aeroflot, Korean (unless they improve, which maybe they will since Delta has now decided to once again share marketing with them), most of the east European former USSR states' airlines, and most of the Central American airlines. LanChile and Varig I would fly, but not Aerolineas Argentinas or most other South American airlines.
The carrier I feel most comfortable (safety wise, not physically) is El AL.