When can a pilot disobey ATC commands?
In case of emergencies, yes. The pilot in command has the final authority and responsibility for safety of the flight and can disobey ATC commands in case of emergencies. The reasons for that and the results will decide the consequences.
From 14 CFR §91.123 Compliance with ATC clearances and instructions:

(a) When an ATC clearance has been obtained, no pilot in command may deviate from that clearance unless an amended clearance is obtained, an emergency exists, or the deviation is in response to a traffic alert and collision avoidance system resolution advisory.
(b) Except in an emergency, no person may operate an aircraft contrary to an ATC instruction in an area in which air traffic control is exercised.

From 14 CFR §121.557   Emergencies: Domestic and flag operations:

(a) In an emergency situation that requires immediate decision and action the pilot in command may take any action that he considers necessary under the circumstances. In such a case he may deviate from prescribed operations procedures and methods, weather minimums, and this chapter, to the extent required in the interests of safety.

Emphasis mine. Obviously, it would be prudent for the the pilot (and required under FAR 91.123(c), as @Pondlife points out) to report the deviation to the ATC as soon as possible.