A standard film length does not exist. There is no maximum length for a feature film, but there are multiple definitions regarding minimum length. The American Film Institute Catalog of Motion Pictures and the British Film Institute both define a "feature film" as having a run time in excess of 40 minutes. The French Centre National de la Cinématographie uses the definition of 35 mm film longer than 1,600 meters (58 minutes and 29 seconds).
Since the late 20th Century, many film editors in the United States and United Kingdom have referred to Alfred Hitchcock's advice on movie length:
The length of a film should be directly related to the endurance of the human bladder.
Hence a common run time of 80 - 120 minutes.
Edit: /u/BonSequitur has written a more thorough answer to this question.
Early cinema had very short (15 minutes and less) running times, but around the 1910s you start seeing experiments in longer films; the most well-known example in American cinema is The Birth of a Nation, which has a bladder-straining running time of 165 minutes. The current (informal) standard of virtually all features running between 80 and 120 minutes (With 100 minutes being a very common target for screenwriters and editors) was arrived at by industry trial and error, and was pretty much solidified in Hollywood when spoken film became the norm. There's no specific reason for it. Audiences just responded very well to the more involved storytelling in feature-length films - So much so that shorts had all but disappeared from theatres in the 1930s, or were relegated to the role of secondary features filling out the running time of a feature-length film.
If you look at it in terms of dollars per running minute of film, movie production gets more efficient as the film goes longer, and people have certain expectations around how much entertainment they're willing to pay for - audiences are generally not interested in going to a theatre and paying money to sit for fifteen minutes and watch a short; in fact, short and "medium" films have historically been billed in groups or alongside other entertainment, to fill out a programme that was an hour long or more. The full-length "feature" just makes financial sense for a multitude of reasons.
Meanwhile, films longer than 120 minutes have always been a dicey proposition; audiences are generally not willing to pay more to see a longer film, even though longer running times mean theatres can schedule less showings - thus, three-hour monstrosities are unappealing for theatres, relative to two-hour movies.
Extremely long "epic" films have been produced, some to great success, but they are exceptional cases; Gone with the Wind and "The Ten Commandments* have running times in excess of 220 minutes, ie nearly four hours. Both were extremely successful films. Both were presented with an intermission mid-film, and both were massive "event movies" tied to changes in the film theatre market (Gone with the Wind is associated with the rise of cinema palaces and upscale moviegoing; The Ten Commandments with widescreen). Both were cultural touchstones for an entire era of film-making. Why didn't four-hour movies become the norm? Probably because for every Gone with the Wind, there is at least one Heaven's Gate - an enormous, expensive, bloated monster of a movie that barely anybody saw, and which theatres quickly pulled in favour of more popular, shorter films.
Running times became even more consistent after the seventies, with the rise of filmmaking as a formal profession. Most American screenwriters in the last three decades have been trained to write films according to a formula based around three-act structure, which in particular prescribes that films should shoot for a 100-minute running time. Market expectations have essentially congealed around that number at all levels. This isn't to say nobody ever deviates from the formula, but people do so for specific reasons; usually, a longer running time is associated with either 1. "prestige" films that are not necessarily shooting for mass market commercial success, but rather for critical credibility that reflects well on the studio's brand; 2. extremely bankable writers and directors making "superlong" films because everything they touch turns to gold and the studio will let them; or 3. both.
I believe you have roughly two camps that have a hand in determining the length of a movie, the directors and the studios.
The director who has enough clout to ensure the completed film is the appropriate length captures his/her vision. From the article below: "...Hollywood’s prestige films often tend toward epic productions, from “Gone With the Wind” and “Ben-Hur” to “Gandhi” and “Titanic.”
The studio, and its desire to ensure the greatest return on their investment. From the article below: "General Hollywood wisdom is that it’s bad business to let a movie run on at the mouth because it limits the number of screenings that theaters can fit in each day, potentially undermining a film’s profits."
Edit: formatting
A comment and a question off the title of this thread:
The current runtime for most films seems closer to 120-140 minutes, so much so that when a film like the new Teenage Mutant Ninja Turtles comes out, it's applauded for being around 100 minutes. Even comedies, usually the fastest and breeziest of genres, (for example, Anchorman 2 is 119 minutes whereas the first Anchorman is a mere 94 minutes).
Is it because audiences think they're getting more bang for their buck with nearly 3-hour installments of Batman, Transformers, and Pirates of the Caribbean. Or is it just filmmaker/studio overindulgence? You'd think they'd push for shorter movies to cram in more screenings.