Eric Brewer's presentation of CAP theorem at PODC (Principles of Distributed Computing) keynote address: Consistency, Availability and Partition to network tolerance - only two of these properties can be possessed by shared data systems.
Consistency + Availability: Single-site databases (2-phase commit)
Consistency + Partitions: Distributed databases (pessimistic locking)
Availability + Partitions: DNS (conflict resolution)
Formally proven in 2002 paper by Seth Gilbert and Nancy Lynch.
BASE (Basically Available, Soft-state, Eventually consistent) is the opposite of ACID.
Verner Vogels article on Eventual Consistency
Great write on CAP here
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