Umpteenth Customer

Congratulations! You're the one millionth customer of Honest John's Dealership! Or maybe you're the ten thousandth customer of the Malt Shop! Or maybe it's just an ordinary shop in an ordinary mall. Well, either way. You are the lucky person that's a milestone of their history: you are their hundredth/thousandth/millionth/billionth customer, and what better way to show their appreciation than to give you this random item?

Expect a shower of confetti and balloons when this occurs, almost as if it was a birthday party. Which it technically is, just for the company.

In reality, for the very very very very few places that actually do this, it'll simply be something small like a commemorative pen or badge. In media, however, this item (or series of items) will be something either extravagant or extremely desired — so, the conflict of the episode will sometimes either be resolved by or revolve around this item.

Examples of Umpteenth Customer include:

Advertising

Spoofed in this early '70s ad for Volkswagen.

Anime and Manga

In Kamen Rider Decade, Tsukasa ends up getting a choice of wife, a modeling job, a gig as a manager, and more simply for being an umpteenth customer. Turns out it was all a plot to make him love the world and stay.
Zig Zagged Trope a bit in the Mega Man NT Warrior manga. There's a scene where Lan is told he's the one millionth customer of a restaurant, so he won a free helicopter ride as a prize. At this point, he and his friend Chaud are on the run from the government because of Megaman's new powers, which they fear. Once Lan goes up in the helicopter, he reveals that he knows that this whole "millionth customer" was a sham, and that this is an attempt to kidnap him and draw Megaman out, but he's willing to do it so that he'll see Megaman again. Immediately turned around, as he really has won the trip and this is a genuine prize, and the pilot has no idea who Lan is.

Comic Books

A Running Gag in Archie Comics seems to be that Jughead would always be this whether it's a restaurant or a grocery store. Thanks to Juggie being a Big Eater, chances are those stores would wind up bankrupt at the end of the day.

Film

In Amazon Women on the Moon, a boy who goes to a drug store to buy condoms (discreetly) for his date not only wins a prize...but becomes their spokesman, much to his horror.

Literature

Inverted in A Song for Arbonne by Guy Gavriel Kay, where every ninth person to enter an inn during the beginning-of-book festival gets thrown in a dunk tank. (Ultimately the joke's on the innkeeper—his regulars filled the dunk tank with his champagne...)

Live-Action TV

An episode of the classic television series Dennis the Menace had an entire plot that revolved around this trope. Mr. Wilson carefully calculated the time at which the something-thousandth customer would go through the line at the local grocery store, with the intention of being that customer and winning a free shopping spree. Unfortunately, he miscalculates by one person, and Dennis ends up winning the prize.
In Doctor Who episode "Delta and the Bannermen", it begins with the TARDIS being the umpteenth vehicle to pass through a hyperspace tollbooth; not only is the toll waived, the Doctor and Mel are awarded free places in an alien tour group going to visit 1950s Earth.
Parodied in a Mitchell and Webb sketch, in which a group of eccentric businessmen wait for the millionth visitor to their website, only to find that he completely ignored all the banner ads and pop-ups telling him this.
In Psych, one of the cold opens begin with young Shawn as the one millionth customer of a super market.
One Supernatural episode involves a rabbit's foot that grants increasingly good luck until it is lost, at which point it grants increasingly bad luck that ends with death. During the good luck run, Sam wins free meals for life at a restaurant. While eating, he loses the foot to a savvy thief. As Sam's luck turns bad, some people are out to kill him—those who can't find him see the press release of his award and know immediately where he is.
Trigger Happy TV once set up a "Millionth Customer" extravaganza outside an adult bookstore and suprised one of the unsuspecting chaps leaving the shop. Said customer hauled ass rather quickly after that.
The Tonight Show: One magician was doing tricks disguised as a supermarket cashier. One of his tricks was to declare someone the millionth customer, then take down a large box with the prize. The box would contain exactly what the customer was purchasing.

Music

The "Weird Al" Yankovic song "Hardware Store": "Every twenty-seventh customer will get a ball peen hammer free!"

Newspaper Comics

In a Peanuts Sunday Strip, Charlie Brown went to the movie theater because it was offering free candy bars to the first 1,500 children in line. He let Lucy ahead of him, and she was the 1,500th child.

Video Games

In Simon the Sorcerer 2, a tattooist gives a free tattoo to his 100th customer. Since your character has no money, you need to talk another character to going first so that you can get the tattoo done free.

Western Animation

In one episode of Arthur, Arthur picks up a Sci Fi Shoot'Em Up video game from a store simply for being an umpteenth customer. His life promptly goes down the drain as he struggles with addiction to the game.
Happens time to time to Donald Duck's extremely lucky cousin Gladstone.
In Doug, the eponymous character enters what looks like a video game store and looks around, only to discover that he's the one millionth customer and has won a Pretendo. Of course, this was the setup for the episode's Aesop.
On SpongeBob SquarePants, a customer gets this for giving Mr. Krabs his millionth dollar earned. He gets no prize; he and the others just get thrown out so that Krabs can enjoy the dollar in peace. He does reward his workers, though... with a fishing trip.
In The Weekenders, Carver orders from the snack vendor and won some prizes for being being the one millionth customer. Tino asks for napkins and end up being the one million and first customer. He won two passes to their favorite band which leads to the episode's plot deciding who to take to the concert.
In The Simpsons, Homer bought the one millionth ice cream cone resulting in him appearing in Kent Brockman's talk show.
On Daria, the eponymous character was the 10,000th customer at the Doo Dad Shop, which sells various novelties. She was dismayed by this, as she wouldn't have gone without a certificate.

Real Life

A great many pop-up/banner ads on the Internet will say, "Congratulations! You are the one millionth visitor! Click here to claim your prize!" (Protip: don't click these.)