The Longest Running Jokes In 'The Big Bang Theory'

The first half of the series shows Penny taking advantage of Sheldon and Leonard's willingness to share their things with her. This ranges from her not paying for any of the food and even having Leonard pay for her rent one time. An extension of this gag features Sheldon constantly changing the WiFi password that makes references to Penny's freeloading nature.

His lack of social skills means Sheldon takes every statement at face value, not realizing when someone's being sarcastic. This reaches the point where he has to ask the person if they're deliberately being sarcastic, and keeping a score of how many times he was able to detect sarcasm.

Sheldon has a compulsive need to knock on doors three times to announce his arrival, as well as utter the name of the person he wants to meet after each knock. During times where the door opens before he says their name, Sheldon freaks out and feels the need to knock again anyway. 

Sheldon's unintentionally rude nature rubs many people the wrong way, whom he takes to considering his mortal enemies. Along with keeping a list of the names of the people he hates, Sheldon also engages in petty acts of vengeance against the likes of Wil Wheaton, Barry Kripke, and having restraining orders against him by famous celebrities.

Sheldon's neurotic personality leads each character that meets him to assume he's crazy, which he's quick to point out isn't the case because his mother specifically had him tested to make sure.

Sheldon constantly brings up the "Roommate Agreement," a set of documents he considers legally binding over his living situation with Leonard. This makes life difficult for Leonard as he has to put up with ridiculous terms as per the agreement. Examples include Leonard agreeing to meet with Sheldon in the past if he creates a time machine, and not being allowed to whistle in the apartment.