If you set all of a mob's levels to 2147483647, It would have a negative level and exhibit some really bizarre traits. For one, It could do no damage, And could never be damaged by attacks.
If you tried to shoot it with projectiles, It would freeze them in midair until it moved out of their way. The only ways these mobs could be harmed were environmental damage. Fire, Spikes, Falling, Etc.
To this day, I have no clue how this worked.
Oh, One other fun bug was in 2.0. Placing a key down and breaking it would yeild a skeleton key. I robbed so many people.
Then there was the 2.1 bug where you could use NPC spawners to edit scripts and give yourself admin. I actually found that bug within a day of the update coming out. I thought about it before I went tosleep and told myself I would try it in the morning. And it worked.