Gladiator Subquest

A staple of many Role Playing Games. This subquest, which is usually an optional Sidequest, but sometimes a part of the main quest, requires you to fight in some sort of gladiatorial combat.

If done as a sidequest, expect rules to make this more difficult than standard combat. For example, you might be limited in your choice of gear, or the fight might include only One party member at a time, or some types of attacks (say magic for example) may be forbidden. Such restrictions are rarer if this is part of the main story line.

Alternatively, it is possible that the player may only need to perform in a few ranks of the subquest to advance the main quest, the rest of the competition is optional.

Main Story examples are usually Inevitable Tournaments, as you are likely to hear of the fight long before you actually have to take part in it.

Adventure Game

 * The Coliseum from Quest for Glory V is the sidequest variant, though no special rules apply.

First Person Shooter

 * Madd Moxxi's Arena of Borderlands is a sidequest example. There is also three smaller arena-like segments as sidequests in the main game. And a fourth one in The Secret Armory of General Knoxx.

Role Playing Game

 * The Coliseum in Final Fantasy VI is an example of the optional version.
 * Final Fantasy VII had the Gold Saucer Battle Arena, where you had to fight one time and afterward became optional.
 * The Arena in The Elder Scrolls IV Oblivion is also an optional version. Your armor is limited to the one provided. You can however use your choice of helmet, shield and weapons.
 * The Hole in Fallout 3's The Pitt DLC is a main story example.
 * Fallout 2 has this in New Reno--you can box for increasing amounts of cash and fame, but the first time you lose, you're done. It's completely optional.
 * You can try again after losing one combat if your speech skill is high enough, though you get reduced pay.
 * And Fallout New Vegas has one as a sidequest in the legion camp. An arena you can fight in (if you are not female).
 * The Munari City arena of Summoner 2 is set up like this. It is part of the main story, but it is possible to return to gain money as a sidequest.
 * Bio Ware loves this trope, to the point where Mass Effect, which otherwise seems to be trying to collect tropes like Pokemon, is so far one of the few exceptions.
 * Not so much anymore as the optional DLC "Pinnacle Station" for the first game creates a quasi-arena like station for you to go against hordes of holographic Geth pretty much solely for bragging rights.
 * The Dueling Rings on Taris in Star Wars Knights of the Old Republic. It is a side quest and the fights have to be fought one on one.
 * The Provings are of the Dwarven Commoner (as a main quest) and Dwarven Noble (as a sidequest) origins in Dragon Age Origins. They return later in the Orzimmar portion of the game as part of the main quest.
 * Jade Empire also has them as a main story quest.
 * The Olympus Coliseum from Kingdom Hearts, and the Underworld from the sequel.
 * The Tolbi Coliseum in Golden Sun.
 * One chapter of Paper Mario the Thousand Year Door is built around this. Unlike the usual story enforced examples, there are rules to make the fighting more difficult. Following these conditions is needed to go up in rank.
 * Radiant Historia has one; only some of the fights are mandatory.
 * Gothic III has several arenas in different towns. Gothic I also has a small one.
 * The remake of Alter AILA has one. It's over 100 fights long.

Turn Based Strategy

 * Fire Emblem has Coliseums where you can have one of your units battle. If you win, you get double your entrance fee, if you lose, the unit you sent dies. You have the option of forfeiting the match, but you will get no refund. Slightly different in Genealogy of the Holy War, where units that lose a fight are left alive but with one HP ; the sum of money earned after each fight is preset ; and instead of unlimited, random enemies, each unit can only face seven fixed adversaries.