In a custom game, I decided to test out how ferocious the Dragon was only to find out... it would never attack me. I'm not certain if this is with every champion, or if it's because I used Twisted Advance on Maokai (untargetable ability when cast) to initiate on him. Either way... I was surprised.
How to Reproduce:
1. Start a custom game
2. Wait for Dragon/Baron to Spawn
3. Attack it, and watch as they don't defend themselves
Pretty funny stuff. (Editted for Baron as well).