If PC games count, in Baldur’s Gate, your party will start bellyaching about waiting around doing nothing. Each character has an audio for “bored”, including your main, and they won’t stop.
IIRC, on the Genesis version of “Aladdin”, if you bring the guards into the picture just far enough that you can see them, but not within attack range, they will stand there and eat donuts.
The earliest instance I can think of is in Starflight 2: Trade Routes of the Cloud Nebula (1989), your little spaceman will tap his feet if left idle several minutes in the main space station. Can anyone find one that occured before that?
IIRC, Maximo scratches his butt.
Duke Nuke’em growls “What are you waiting for, Christmas?!?”
Does anyone else remember a game called Boulderdash, in which you’re a little creature tunneling through earth to get jewels and avoid getting squashed by boulders? I seem to remember that the character would stand there and stamp his feet with his arms crossed if you did nothing for a while.
Great game, by the way.
Slightly off topic, but something I found amusing in Warcraft II. Whenever you click a character to activate him, he responds with “Yes, sire?” or “My liege” or something like that. If you kept clicking him without doing anything else he’d eventually scream, “WHAT?!?!” 
I remember that one. It was supposidly the sequel to Bubble Bobble. I loved that game.
All the Warcraft games and Starcraft have a whole series of things the characters say. They’re often self-referential, like “Easily amused, aren’t you?”.
In WarCraft II, there was exactly one female character. Keep clicking on her, and eventually she would say, “You don’t touch the other elves that way…”
WarCraft III included such gems as:
Elven Archer: “Shot through the heart, and I’m to blame!”
Dwarven Hero: (Scottish accent) “Ach, there’s nothing more invigorating than going into battle with a baaad hangover!” (or something like that)
Human peasant: (village idiot accent) “You’re the King? Well, I didn’t vote for you.” “Help! Help! I’m being oppressed!” “We found a witch, may we burn her?”
Undead somethingorother: “I eat dead people!”
The Dryads sound like California bleach-blond airheads, and say the kinds of things you’d expect from bleach-blond airheads.
continuing the off topic, in Warcraft II, during installation, there is an option to test your sound card. you click a button and the voice of a footman goes, “Your soundcard works perfectly.” keep clicking and the button goes, “Enjoying yourself?” more clicking, “It doesn’t get any better than this!”
What am I, chopped liver? 
This…is…my…BOOMSTICK!
I haven’t played a video game in ages.
I do know that the Office Assistants (if that’s what they’re called) on Microsoft Office programs do certain things when left idle. The paper clip’s eyelids droop when left with nothing to do, for example.
Sorry… I offer only what I know.
To me, with Warcraft being off topic and all, the absolute king is Klaymen, the hero of “Neverhood”.
He does a whole bunch of stuff when bored. I can recall only one of them right now, but it’s a good one: He rips off his head and, holding it in one hand, proceeds to have a puppet theatre style conversation, using bad ventriloquism to make his other hand ‘speak’ (No actual words from either of them, just babbling). He then puts his head back where it ought to be.
In the C&C games, the soldiers will often figit, do pushups, etc if left alone for a while.
In World of Warcraft the human female gives a full bodied shoulder shrugging exasperated or bored sigh, much like you’d see a self absorbed young female give when not being the center of attention when she wanted to be.
The night elf female bounces on her toes ina “I’ve got too much energy and let’s get moving” sort of way. I can’t think of the others at the moment.
Every now and then I notice that the NPC’s and baddies have fidgets too. I find them highly amusing. The troggs scratch their bum. There’s an ogre that passes gass and pops the gas bubble. There’s an undead or some other skeletal sort of baddie that takes his head off and plays with it Harlem Globetrotter style, rolling it back and forth across his shoulders. The wolves in the forest chase down the rabbits and kill them. If you kill the wolf afterwards you find a rabbit’s foot as part of the loot. Lot’s of the NPC’s pace and the caster baddies buff themselves even when you are way out of range.
Also in World of Warcraft, the Succubus will whip herself (I think) and say, ‘ooh!’.
It gets kind of annoying when you are crammed in the auction house with 50 other players, and the other warlocks’ succubi are all doing this, between all the constant whipping and moaning sounds you’d think you were in an S&M club
The bubbles are a traditional Japanese cliche that shows up in a number of video games. Whereas we use “Zzz” to represent someone snoring, the Japanese use a booger or something that expands and retracts in one’s nostril.
In Ambrosia Software’s Farazel’s Wand, Farazel will look at you disgustedly, tap his foot, wave his arms around, and eventually start dancing if you leave him alone. Both Halo: Combat Evolved and Halo 2 have brief scenes of the Master Chief fiddling with whatever weapon he happens to be holding. The Sims characters would sometimes “look” directly at you and make an appeal to have whatever problem they were experiencing fixed.
I think N64 Link swings his sword a little too.
I’ve seen the C&C fidgets too, IIRC one of the guys cleans/works with his gun too.
And of course if you leave Sim City running, fires, riots, floods, tornados can happen, or if you’ve them switched off you just earn money through taxes 