An airline is not necessarily liable if your flight is delayed or cancelled. "Acts of God," like bad weather, are deemed beyond the carriers' control. When delays or cancellations are caused by the weather, they will usually refund your ticket, even if it's nonrefundable, but they won't necessarily be responsible for any inconveniences suffered.
The following is a list of other situations where the airlines can legally deny you boarding, or remove you from a flight on which you are confirmed:
# If you refuse to permit a search of your person or property for explosives or a concealed deadly, or dangerous weapon.
# If you refuse to provide positive identification or don't have proper documentation for travel across international boundaries.
# If your conduct is disorderly, abusive or violent. (In addition to removal from a flight, the FAA may also propose fines up to $25,000 per violation in cases of passenger unruliness.)
# If you are barefoot; if you are unable to sit in the seat with seat belt fastened; if you are intoxicated or under the influence of drugs; if you attempt to interfere with any member of the flight crew; or if you have a concealed or unconcealed deadly or dangerous weapon.
# If the airline must comply with any government regulation of space or request for emergency transportation in connection with national defense or national disasters.