http://tvtropes.org/pmwiki/pmwiki.php/Main/ASinisterClue

Batman: Left-handed...

Jack the Ripper: Oh, the nuns beat that wickedness out of me. Always use my right...except for Jack's work. Batman: Gotham by Gaslight : Oh, the nuns beat that wickedness out of me. Always use my right...except for Jack's work.

A very old trope, in which left-handedness is a signal that that someone is the Villain or The Mole, or occasionally just susceptible to the Heel–Face Revolving Door. This only counts when somebody is specifically mentioned as being left-handed, not just because an actor is left-handed.

Have some Trivia - The word "sinister" actually is derived from the Latin word for left-handedness, and also related to the Bar Sinister which is a symbol of bastardy, and thus untrustworthiness.

This is also related to Evil Twin; twins do often have opposite dominant hands, and an Evil Twin will (almost invariably) be the left-handed one.

Additionally, in older times, left-handedness was often a sign of evil or trickery because of the fact that people would shake hands with their right, grabbing each other by the wrists, in order to show that they were friendly and didn't have weapons. Of course, this is incredibly small-minded since if left-handed people were in the majority then it would be the other way around. Still, a lefty could shake with their right hand, grasping the other person's dominant hand, and attack with their weapon in their left hand while the other was defenceless - or even steal a rightie's weapon more easily. Also, during the Middle Ages, towers were built so defenders would have no problem swinging their swords down staircases while attackers would have more difficulties swinging up - and staircases are still built this way to this day. However, this only applied if both were right handed; if the attacker were left-handed, the two would be evenly matched.

In many cultures, before the invention of toilet paper and forks, the right hand was used for eating, greeting etc., while the left hand was used for wiping and other less savory things. In some places, being left-dominant was a sign that there was something inherently 'wrong' with the child, to the point of demonic possession, and to this day some parents will tie a left-handed child's hand behind their back until they learn to be ambidextrous. Ironically this will not change the hand that you instinctively lead with in your daily interactions.

Another related trope is for a character to lose his right hand, symbolizing his loss of a moral compass. This can presage a Face–Heel Turn by the Hero. It is also common for Mad Scientists to have a mechanical right arm. Alternatively, the left hand might become the repository of Sealed Evil in a Can. Compare Red Right Hand.

A subtrope is The Killer Was Left-Handed, where there is actually evidence that the killer was left-handed. Examples of that trope should go there.

The opposite, when left-handedness is viewed favorably, is The Southpaw. Sometimes overlaps with Left-Handed Mirror. Also see I Am Not Left-Handed.

Examples:

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Anime & Manga

Comic Books

Green Lantern: Eventual villain Sinestro wears his power ring on his left hand.

Films — Live-Action

Gamebooks

Inverted (thematically at least) in the Lone Wolf gamebooks: magic traditions inspired by the Forces of Light are referred to as "left-handed", while the Black Magic of the servants of God of Darkness Naar are referred to as "right-handed".

Literature

In The Bible, Ehud, one of the judges, actually managed to assassinate a king by hiding a miniature weapon on his right hip. Thus the weapon wasn't found, and he could still use it, being left-handed.

Arya from A Song of Ice and Fire. When her dominant hand is revealed to her fencing master, he reacts favorably because fighting left-handed will reverse her stance and movements, which will help confuse her opponents. However, her left-handedness might also be A Sinister Clue about her future, training in a cult of assassins. Subverted with Jaime Lannister, who loses his right hand just before his Heel–Face Turn , away from the dark side

In the novel The Sterkarm Handshake, the whole Sterkarm clan are lefties and are known for being backstabbers.

Inverted in the Goosebumps book Let's Get Invisible. The narrator's brother is left-handed, so seeing "him" pitch a baseball