3 times Mjolnir has been broken. 

1.  Thor vs. The Destroyer 

From Journey Into Mystery #118

A pissed off Destroyer fires a blast that slices a large chunk off Mjolnir.

2.  The Avengers vs. Molecule Man

From Avengers #215

The Molecule Man captures the Avengers and Silver Surfer and uses his powers to simultaneously destroy Captain America’s shield, Iron Man’s Armor, Silver Surfers board and Mjolnir.

3. Thor vs. Bor 

From Thor vol. 3 #601

Under Loki’s spell, a resurrected Bor and Thor do battle.  Thor delivers the final mighty blow with such force that part of Mjolnir shatters.