Here are the fates of all the ships named Enterprise (not counting alternate timelines)
NCC-1701: Auto-destructed above the "Genesis Planet" (Star Trek III: The Search For Spock)
NCC-1701-B: Fate unknown (presumed destroyed)
NCC-1701-C: Destroyed fighting the Romulans (Star Trek: The Next Generation, "Yesterday's Enterprise")
NCC-1701-D: Destroyed in the battle of Veridian III (Star Trek: Generations)
NCC-1701-E: Active as of 2379
If we're talking about techincal destruction, as in being destroyed in action as opposed to merely being decommissioned, then the answer is three: the NCC-1701, the NCC-1701-C, and the NCC-1701-D.