What comes to my mind is Tom Bombadil in "The Lord of the Rings, The Battle for Middle-earth II"
or the nudie cards in The Witcher or perhaps the entire Japanese faction in C&C Red Alert 3

In games Acromage comes to mind.

In Tarantino's movies 90% of dialogue, nothing to do with the plot, but smart and interesting.

Flatout, the whole game.
Duke 3D, the strippers.

Oh yeah, almost forgot, every easter egg in every game ever made.

Bombadil, the Jar Jar Binks of Lord of the rings. Just so annoying.

How about the taunt button in the Evil Dead games... So you can mouth off catch phrases whilst ripping deadites to pieces! "Hey look, I created a cure for ugly..." BOOM!!!

Reading your email in Nethack?

E.Y.E. is a definition of what you are describing. Most of the 'features' of the game either make it harder or are rightaway hindering you, but you can deploy a sentrybot, hack an enemy and look behind the wall trough his eyes then possess him, use sound triangulation to spot exact location of enemies and combine it with a heavy, piercing sniper rifle, sneak past enemies and explode their brains from remote locations, dispatch sentry turrets and get a bunch of enemies following you, hack automated defences and kill defenders using those... That game is just ... Uh.

Any games with quicksaves.

Quicksave > Rampage > Brush off dust > Quickload > Continue game.

The reactions of your units when you press on them more than once in Warcraft III. STOP POKING ME !!!!

Sonic the Hedgehog tapping his foot if you don't press any buttons for a while.

That reminds me - Dungeons of Dredmor! If you go idle there, your character whips out a handheld and starts playing it.

Books, in Elder Scrolls.

Some scifi FPS had full games in arcades (including some ultima-like RPG), you could play them for hours. I don't remember what game it was, though. I love games-in-a-game.

NOLF has these henchmen digressions you can listen to, and the unused file of a piaf song.

Shadow of the Comet had a full Lovecraft museum.

Evil Genius has traps that you can build in your corridors to harm enemy agents (not that it has any usefulness).

There are a few like that. I can't remember, maybe it was Megaman or Rayman actually use to go to sleep.
Oh, La Mulana, when you pause he gets out a book and starts reading.

I'd say :

In Tarantino's movies 90% of plot. Nothing to do with the dialogues, but thrilling and enjoyable.

Speaking of which, is there not a Quick Save for Gothic 1 or am I just too stupid to find it?

its so much fun to control Bombadil in the game singing happily while causing so much destruction and mayhem (i haven't seen or read the hobbit so i don't know what hes like in those other mediums)