Appeal To Popularity

Also called

Argumentum ad populum ("appeal to the people")
Appeal to Common Practice
Quality by Popular Vote
Any relevant population figure (sixty million Frenchmen, a billion Chinese, etc.)
Common Knowledge
Sheep Factor
Five Billion Flies (as in "Eat shit, five billion flies can't be wrong!")
Democratic Fallacy
Everyone Knows...

The appeal to popularity is built around the belief that something is true (or false) because a lot of people believe it is. This is fallacious because it confuses whether an idea is justified with whether it is accepted. Demonstrating widespread support for something only proves it is popular, not that it is true.

Alice: Don't you know smoking's bad for you, Bob?
Bob: Bah, it's just propaganda. If it were really bad for you, why would millions of people do it, hm?

This is the standard version; the belief that a large group is incapable of being incorrect. The fallacy can also be inverted, however, with popularity being taken as a sign something is wrong:

Bob: Alice, what's that terrible noise coming out of your speakers? I thought you liked The Band.
Alice: Geez, get with the times, The Band suck since they sold out and went mainstream.

The latter logic underlies It's Popular, Now It Sucks, and is often used with regard to "edgy" media.

Examples of Appeal to Popularity include:

Live Action TV

On Have I Got News for You, Louise Bagshaw argued against the Alternative Vote method based on the fact that very few countries use it. This prompted Ian Hislop to point out that much of the world is starving, which is a pretty strong argument against eating.

Real Life

Lemmings are a prime example, as well as an Appeal to Authority. If everyone, including random authorities, say that lemmings commit mass suicide.... The truth: Stoats. (Not to mention that a famous lemmings-jumping-off-a-cliff video, as filmed by Disney, had people off-camera herding the lemmings over said cliff. This isn't as horrific as it sounds, because lemmings fall slowly enough to be unharmed by the fall, but still dodgy.)
Lots of "common knowledge" surrounding various animals survives because of the appeal to popularity.
- The idea that the adult sizes of fish and reptiles are determined by tank size falls into this.
- As does the idea that birds won't take back hatchlings that smell like humans (fun fact: very few birds actually have a sense of smell acute enough to notice if their baby smells strange).
- This is also why people think piranhas are solely carnivorous. In fact, they're omnivores, and eat primarily insects, seeds, and other fish.

Western Animation

"The Mob Song" from Beauty and the Beast includes the line "Here we come, we're fifty strong and fifty Frenchmen can't be wrong".
- Well, they're French, of course they would say that.

Looks like this fallacy but is not

If the investigated subject isn't an objectively measurable thing, but a social concept, that is indeed determined by popularity. For example:

"Gold is valuable because many people pay for it."
""Trope" is a word meaning "storytelling device", because that's how most people use it."
"Most people would agree that is improper to talk in the cinema during a movie, so don't do it."

These concepts, like economical value, linguistic meaning, or etiquette, are things that only exist because a large number of us believe that they exist. If everyone would believe that gold is worthless, its value would disappear (this happens at the beginning of the novel Galapagos).

Election of an official. John Doe is President because he got the most votes. Voting was the method for determining presidency according to the Constitution, it is no more stupid then most political methods, and has the advantage of getting the greatest number of people possible on board with the new government. That is, not an ideal method of divining desirable qualities in someone, but a moderately foolproof method of resolving disagreements with limited amount of fuss -- in much the same way as duels, or "you win the right to actively participate by investing time and risk" political system from above-quoted Starship Troopers.