Appeal to Tradition

The polar opposite of Appeal to Novelty, where the older position is right. See They Changed It, Now It Sucks, Nostalgia Filter, Older Is Better, and Good Old Ways. This tends to be rolled out regarding consumer products and morality; in the former case, they don't make 'em like they used to, and in the latter, it was better in the good ol' days.

Granted that "old ways" usually tend to be at least adequate, or nobody sticks with them long enough for them to become old ways in the first place (according to Lindy Effect heuristics, if something worked for X years, it can be expected to go on for another X years); what makes this a fallacy is the untested assumption that no further refinement or improvement of the process is possible (it will work well forever without any changes).

Also called

Appeal to Antiquity.
"We've Always Done It This Way."

Examples of Appeal to Tradition include:

Advertising

A commercial for the allergy medicine Claritin bragged that "while other brands have recently changed their formulas, Claritin chose not to change", leaving out that, when many companies change formulas, it's usually for a pretty good reason (e.g. dangerous ingredients). Well, when it's not just to keep their patents going, anyway.
Blue Bell claims to 'taste just like the good old days'. Its commercials also include a lot of old timey things.

Comic Books

Almost any significant change to an existing comic-book character, such as a new costume, seems to be greeted by loud choruses of this nowadays.

Literature

In "The Lottery", this is how the townsfolk justify the eponymous event. They're appalled that nearby towns have given up the grand old tradition of stoning a randomly selected person to death, because it's what they've always done.
In the Discworld novels, used to justify pretty much everything the Unseen University does. In The Science of Discworld, when Ponder Stibbons has a radical new idea, he has to claim he got it from a book a few hundred years old for the faculty to take him seriously.
There's a similar situation in another Discworld book Pyramids; the pharaoh's time is spent carrying out rituals, and the whole country is being held in a sort of stasis because the pyramids are recycling the same bit of time over and over.
In the Gormenghast books, so many traditions have grown up around the castle and its ruler that the Earl must spend virtually his entire life carrying out one pointless ritual after another, leaving only an occasional hour before bed in which to do something because he wants to. Many of the castle's servants are born into their professions, and trapped in a similar bind. The court even includes a "Master of Ritual", a sort of Grand Vizier whose entire job is to keep track of all these traditions.
In Rivers of London DCI Nightingale's defence of The Masquerade pretty much comes down to we've always done it this way. To say Peter is not impressed would be an understatement.

Music

"Weird Al" Yankovic's song "Weasel Stomping Day" is about a fictional holiday where people spread mayonnaise on their lawns, then put on viking helmets and hiking boots in order to crush weasels to death. Complete with tongue-in-cheek lyrics such as "It's tradition, that makes it okay" in order to mock the idea that an abhorrent act is acceptable if it is 'traditional'.

Video Games

Deconstructed in Final Fantasy X, as the people of Spira rely solely on the tradition of the Grand Summoner and their pilgrimages in order to defeat Sin and bring about The Calm (the period in which the populace can live without fear of their villages being randomly destroyed by an evil whale-thingy). However, this only lasts for a few years at most, so Sin would return again, and perpetuate the 'spiral of death' that the land is caught in. In addition, the machina-using Al Bhed, the only ones who challenge the ritual because of what happens to the summoner in the process, are ostracized by the rest of society, as they believe that Sin was born because of the use of machines.
Older gamers and fans of older games often respond this way to games that experiment with new features or new spins on existing video game tropes. If the game fails, it will be because the makers tried to break a video game tradition going back to the NES era.

Web Comics

In Goblins, this is Young-and-Beautiful's reason for not letting the goblin tribe use their magic items.

Young-and-Beautiful: For countless generations we have done things a certain way. We can't do everything differently now because it... "makes sense".

Western Animation

Illustrated in The Simpsons episode "Whacking Day", where snakes are herded to the town square and beaten to death with clubs. Lisa and Barry White are the only characters who are initially disgusted with the idea.
Family Guy: Pepperidge fahhhrrrm remembers.

Real Life

Often used in political debates, especially about social issues. And we'll leave it at that.
The British general Sir Charles Napier, during his deployment in India in the 1840s, attended the funeral pyre of a local dignitary, when he, to his horror, saw the wife of the deceased being led onto the pyre. Napier ordered his men to intervene and hang the offenders. When an outraged local priest asked by what right he had killed men for following their people's tradition of burning widows alongside their dead husbands, Napier answered: "My people have a tradition of hanging men who attempt to murder women".
Often used as an aesthetic point. In that case it is not a fallacy because it is not an argument at all. Who says tradition is not beautiful? Well, people who don't like tradition obviously, but enough people do think it beautiful.