Second Prize

"First prize: a one week trip to Pittsburgh. Second prize: a two week trip to Pittsburgh."

A character enters a competition and wins—but not the prize they were hoping for. Usually they are either hoping for the first prize and get second, or vice versa. May be used as anything from a throwaway gag (e.g. the Futurama episode in which the Lead In has Bender enter Zoidberg in a pet show) to the entire premise of an episode.

Compare Second Place Is for Winners.

Examples of Second Prize include:

Anime and Manga

Keroro Gunsou episode 18 has Keroro entering a Kansai-style comedy contest in order to win a rare Gundam-knockoff model kit. He wins mainly through underhandedness and alien technology; he learns too late that the model is only the participation prize, and first place gets a fridge, but he's too much of a show-off to throw the contest.

Film

In Children Of Heaven, an Iranian movie, the main character (a boy) wants to get another pair of shoes for his little sister, since they share a pair of shoes, by entering a track and field competition. He aims to be number ~~two~~ three, the prize is a pair of shoes, but ends up being the first, ruining his current shoes.
- Good thing their dad was shown buying two new pairs of shoes for the kids.

Literature

In one of the Milly Molly Mandy stories, Milly-Molly-Mandy has her heart set on a toy rabbit that is one of the prizes in a competition. She tries so hard that she wins - then discovers that the rabbit was the booby prize. She gets the rabbit in the end by swapping her prize with the loser.
Robert Heinlein's Have Space Suit--Will Travel: Cliff Russell enters a contest where first prize is a trip to the moon. He wins one of the consolation prizes: a used space suit.
In one of the Encyclopedia Brown books, Encyclopedia Brown must prove that a contest participant delberately lost on the last question to get second place because they'd accidentally broken the grand prize.

Live Action TV

Subverted in an episode of Chef, where Gareth begins bemoaning the unfairness of it as he places second in the hors d'oeuvres section. This is compounded when he places second in the entree section. He is barely able to suppress his rage when he receives third place in the dessert section. He then discovers he was the only contestant to place in more than one category, and has won the overall first place.
An episode of Monk has a man deliberately giving up first place because he wanted the runner-up prize of pie.
Buffy the Vampire Slayer: Subverted for comic effect in an episode in which Cordelia and Buffy compete for the title of Homecoming Queen. As expected, the two descend into vicious (albeit hilarious) rivalry, find themselves in danger, pull together, etc. The writers save the high school cliche through outright parody: CORDELIA: "You know, after everything we've been through, this whole question of who gets to be homecoming queen seems..." BUFFY: "Pretty damn important!" CORDELIA: "Right!" In the end, Sunnydale High awards the prize equally to two people in its first-ever tie. Luckily for us viewers, those two people aren't Buffy and Cordelia, but the two other girls who were competing against them. Buffy and Cordelia leave the auditorium in disgust.

Video Games

The 'don't get the prize you wanted' version actually appears in both Final Fantasy X and Final Fantasy X-2 with the Blitzball minigame. In both cases you'll often want the 2nd or 3rd prize instead of the first as the better moves and skills for the minigame are rarely the first prize, essentially forcing you to lose games to achieve this.
In Leisure Suit Larry 6, Larry is recruited as a contestant on a rigged game show. He ends up winning the second prize, two weeks at a health spa and resort, which is where the game is set.