Having gone through a few questions asked here, it seems the Joker (Has the Joker ever been inside the Batcave?) has never been in the Batcave, but Catwoman has (Has Catwoman been to the Batcave before New 52?). It made me wonder how many other (super-) villains have managed to get into the Batcave (Silver Age)?
closed as too broad by Valorum, DavidW, Chenmunka, Jenayah, TheLethalCarrot May 27 at 10:54
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In the LEGO multiverse in Lego Batman 2, The Joker and Lex Luthor break into the Batcave and use there anti black stuff ray to destroy a bunch of stuff.
In Batman Arkham origins Bane breaks into the Batcave and destroys Batman's computers then somehow injures Alfred and puts a boulder on top of him (the boulder bit you don't see, though its just after you return in the batwing and see the Bat-cave terminals all broken.
In the animated movie of "Batman vs Robin" the court of owls break into the Batcave and Batman and Nightwing fight them off with "quite the troubles" at not being able to stop them.