Has there ever been a video game that...

…(with your permission of course) takes control of your printer or web camera or browser history and such to create a more immersive experience?

Not to much knowledge, though Eternal Darkness pretended to mess with your Gamecube and TV, though it was simply faking it.

Metal Gear Solid messed with your PS1, sort of. It read your memory cards and commented on saved games and I think it did something like made you switch controller ports as well.

Lose/Lose

Cameras are often used in augmented reality games.

“Vib Ribbon” let you insert a CD and would generate levels based on the music.

The character Psycho Mantis did that:

There was a game had you running around your directory tree shooting and fighting a virus attack, and it would throw up audio and picture files it found as you ran around. I can’t remember what it was called though - I don’t remember the name, I just remember the controversy when the game found… hidden pictures.

I remember that! Audiosurf is a more modern take on that (gameplay is much different though).

The Monster Rancher/Farm series created one of hundreds of monsters based on the CD/DVD you put in. It was based on some algorithm, except certain albums/games/etc. gave you specially programmed ones.

And of course some Android/iOS games scour your Facebook or similar if you give them permission.

Psycho Mantis could “read your mind” and anticipate moves, but you could hide from him by switching to the second controller port, then he would complain about your mind being hidden. IIRC it wasn’t necessary, but made the battle a lot easier. MGS2 did something similar were the computer system was tweaking out and it gave a false “Fission Mailed” (sic) screen.

There is, of course, the DOOM task manager.

Edit: For real, a nice example is Black and White. Whenever a villager died, a somewhat creepy woman would whisper deeeeath, however, if your name (entered on creating a new game) was on a certain list, it would whisper your name sometimes instead.

However, it did more. Without your permission it would scour instant messanger contact lists on your computer, and actually name villagers after your friends. You probably wouldn’t notice most of the time, but if you did…

Not sure if this applies, but the PC game Majestic was played by phone, email, AOL Instant Messenger, BlackBerry messages, fax, and by visiting special websites.
Supposedly, it was inspired by the Michael Douglas movie The Game. It was an innovative concept that never took off.

The PlayStation 3 has a “game” called EyePet, where it uses the camera and Move controller to generate a little pet on the screen, which is otherwise a live picture of your floor. You interact with the thing using the Move controller.

That is a very cool idea for an ARG.