Someone who's wanted for Hoo-Hahing is bound to be a real threat.

Storm's Will of the Godess super in X-Men Legends 2. 45 seconds of invencibility for all party members plus an increase of 25% to max mana when maxed.

Or Sunfire's Rising Sun super, 45 seconds of invencibility plus a 2x damage boost for himself.

In Fallout 3 and NV there's a cinematic turn based mode (vats) that allows you to enter in a window displaying your enemies while being invulnerable to them. It took me a while to find it and when I did I thought it was so cheap and so gimmicky like what was the point in including this feature in a game you are primarily supposed to kill things in real time.

The Canadian Super Bear with Lazer Eyes from Age of Mythology, or Lazer Bear to be more specific. That thing is unstoppable. Only one power can block him, and that's the God Power of Traitor. And that ability appears only in the expansion.

Big Blue Blob (EU3)

Actually, it's a very patriotic Grizzly Bear. Look at this fanart I found:

You are not invulnerable while using VATS in New Vegas, though :P

The player.

Sneak skill + Bow in Skyrim. Removes all challenge from the game.

One Man Army Noobtube in Modern Warfare 2. That shit gives me nightmares.