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Why does the Terminator wear sunglasses?

"To look cool."

There is another answer. When someone fires a gun, the natural reaction is to blink (next time you watch a film, look for someone blinking on firing the gun!). Obviously being a cyborg, it would be a bit odd that he was blinking all the time so I think that is another reason for it!

There are two well known actors who never blinked on firing a gun, Clint Eastwood and Yul Brynner. I've added a related link.

Another reason could be that the Terminator severly damaged his face during a car accident in the first movie; it left his metal cyborg eyes exposed and clearly showed he was a Terminator. The sunglasses hide the cybornetic eyes. Plus its so freakin badass.

It goes further into the canon than that.^

It is meant to hide the unnatural movement of the eyes. A terminator scans its environment thoroughly. An infiltration unit would be of little use if it caught people staring at its jerking eyes.
Posters and scenes in the media also suggest that their "eyes" tend to and are able to glow past their organic camouflage, being the eyeballs. Sunglasses hide this.
Later Terminator series were able to have free will and establish a personality thanks to their neural net processors. Much of it is subdued by limitations put on by Skynet. John and Sarah Connor were able to override those limitations by resetting their T-800 guardian's chip in Terminator 2. The sunglasses suit the Model 101's style and programmed choice of attire, it being an intimidating biker thug. It can be argued that the Model-101 also possesses an attachment to the sunglasses in which if they are destroyed, the Terminator goes into a sort of "anger" mode in which it will attack the enemy with its full capability or continue on with the mission in a hasty manner as suggested by commentary in the movie.
Examples: Arnold pushes the female cop to the floor with a devastating head blow from his hand.
The T-800 begins repeatedly smashing the TX into nearby walls in a quick manner.
Both T2 and T3 display an angered an annoyed face from Arnold upon the destruction his sunglasses.
It is meant to imply the notion to the viewers as a "Oh no they didn't!" appeal.
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