In any game that offers the player a selection of multiple options to play as (whether it be characters in fighting games, cars in racing games, factions in strategy games, or whatever), Competitive Balance comes into play. Since these options are meant to compete directly against each other, they need to be roughly equally powerful, or else you run into the problems with Character Tiers.
Common ways to competitively balance:
In One Piece: Unlimited Adventure for the Wii, there exists a 2p battle mode where characters can fight each other. The game is straightforward about who is the strongest, with the character tiers being ranked from 1 to 5 — however, the game's "competitive balance" is off. Usopp is only a 3, yet he's the only major character to have ranged attacks, close attacks, a useful "run away attack" (where he runs and drops Spikes of Doom), AND two unusually powerful ultimate attacks, making him a VERY lethal joke character if you're good enough with him and great for boss battles. We've also got Lightning Bruiser Luffy himself, who's an unmatched Game Breaker in Gear Second, and possibly the straightest Mighty Glacier EVER, Monster Chopper — he has just 3 incredibly powerful attacks but can only walk deathly slow. Finally, while not intentional, some characters who are meant to be weak can actually deal alot of damage, making several characters a Glass Cannon (Nami, aforementioned Usopp, Chopper, Bon Clay, etc.).
Burnout 3 plays The Joke Character with a car. In most games, you can get yourself some multplayer bragging rights by picking a slow car. There's a car in Burnout 3 that doesn't only have to be unlocked, but also doesn't move. At all. Now that's taking it to an extreme, people.
Most of the "older" cars (i.e., the Gangster/Carson Grand Marais; the Classic/Hunter Manhattan) aren't quite the fastest cars around, but they certainly have their good points. In the right hands, they can be a Lethal Joke Character.
Street Fighter has a pretty big power gap between the low-end and high-end characters too (Akuma is capable of sinking an entire island and sending people to Hell, for example), but at least the weakest characters in those games are still stronger than the average human!
In game, however, there's really not all that much of a balance gap (though occasionally you get some accidentally broken characters, such as Guile in Street Fighter II and his mystical "Magic Throw" and "handcuffs" glitches, not to mention his insane range and priority; Zangief could also apply, with his extremely powerful throws). Akuma, for instance, is actually fairly fragile, taking the most damage of any of the characters in most of the games where he's a standard character. This is especially prevalent in games such as Tekken, where tournament play is the general focus: In Tekken Tag Tournament, while Ogre and True Ogre might be bosses of death, they're still balanced enough that you can generally beat them with anyone you know how to use correctly. The only exceptions to balance appear at the lower levels of skill, where certain characters are easier to use than others (try using Guile as a beginning player, without a good grasp of charging; and after THAT, you need to learn how to do jump in combos in order to really use him).
The plots of Type Moon's Melty BloodFighting Games are driven by the reality-warping Night of Wallachia. This crazy phenomenon is used to justify Miyako's leap from martial arts student to prime Street Fighter candidate. More amusing is Kohaku and Hisui's transformation from simple maids into Martial Arts and Crafts masters capable of fighting half-demons and ancient vampires.
In the Deadliest Warrior game, you have Guerillas (e.g. Ninja and Apache) who can't get into a direct fight and have to use their agility to survive, Berserkers (e.g. Pirate and Viking) who have a deadly offense, but less in the way of defense, and Balanced fighters (e.g. Knight and Spartan) who can dish out a lot of damage and take it, but won't move very quickly.
First Person Shooter
In most FPS games with class systems, such as Battlefield Heroes, sneakier and faster classes will be weaker than slower, more brutish classes (Heroes's Commando to its Gunner, and Team Fortress 2's Scout and Heavy, for instance), with classes in between (Both BF Heroes's and TF2's Soldier.)
More specifically, one can generally find the Jack of All Stats in the Temjin and Apharmd lines, with the former being simply well balanced and the latter being absolutely brutal at close range. Representing the Fragile Speedster are the Viper and Fei-Yin series, both of which are smaller and agile, but can't take hits very well. In early games, the Belgdor and succesors offer examples of Glass Cannon designs, being somewhat fragile but possessing great hitting power. Bal series are Squishy Wizard, with overall low stats but have nasty trick for those who can master their Attack Drone (including AI). Finally, the Raiden and Dorkas are clear Mighty Glacier most of the time, being among the largest and most powerful but least maneuverable designs in the series.
The Armored Core series sees just about every possible facet of this system, and (at least, after a bit of trial-and-error with regulations files) it generally avoids Game Breakers.
However, in 4 and FA, just about every AC can be considered a Lightning Bruiser in comparison to previous games due to the fact that they typically have at least two or three times the AP of their predecessors, much more powerful weapons, and ridiculous speed (this was taken to Super Robot Genre heights in FA).
Mr. Driller has a total of 7 characters, each one with their own stats; it varies from characters with slow speed but slow air cost, to speedsters with fast air cost rate.
The (currently) 40 usable planets in Meteos differ in nearly every aspect, from the types and quantity of Falling Blocks present and the speed they fall to playing field width and quantity of garbage blocks both sent and received. There are many more differences dealing with game mechanics specific to the series, but suffice to say that separate strategies are needed playing as and against each planet. Each game to date has illustrated this by having the blocks take different appearances for each planet. In the original DS game, for instance, Freaze's blocks look normal but are frozen over, while Gigagush takes on an 8-bit style with animated blocks resembling Space Invaders. By Meteos Wars, every planet has been pretty well balanced with a few exceptions, under normal circumstances.
Atlantica Online has many kinds of characters, each not only with different roles, but also effective or weak against certain other characters or formations.Forming a balanced, universally efficient team is nigh impossible thanks to the ever-present Tactical Rock-Paper-Scissors.
World of Warcraft has ten character classes with three talent trees each, making for a total of 30 builds to balance against each other in small group PvE, large group PvE, arena PvP, and battleground PvP, across 85 levels and 12+ tiers of gear, and this doesn't even count variant builds and racial bonuses. That this task is impossible is mitigated only by Blizzard's determination to try, and balance has consistently improved over time despite the protests of the fanbase. Dueling, or one-on-one PvP, is the sole place they've disclaimed attempts to provide perfect balance, as that would inevitably lead to all classes being the same.
Scout [Ken/Nuri] and Hana [Erika/Hana] in Pangya - The Mario and The Ken (appropriately enough) as they are the starting characters for male and female players.
StarCraft uses this as well. The Terrans are a mixture of Glass Cannons and Jacks; per unit cost, their units have less HP than any other, but they can do fearsome damage. The Protoss are a combination of the Mighty Glacier and Squishy Wizard; their units have the highest HP per-unit-cost, and their spellcasters can be game-changing. The Zerg are naturally Fragile Speedsters, but with some attributes of the Glass Cannon. Their units are cheap, fast, and fragile, but per-unit-cost, they do lots of damage over time. Their speed extends even into how they produce units. The Protoss and the Terrans have production buildings that can make one unit at a time each; the Zerg have a production building that can make 3 at once, and they'll have lots of them lying around since they need them to expand. The Zerg also produce all of their units from the same place, so they can quickly adjust strategies and change up their army.
Interesting in that their play speeds are inverted when it comes to building structures. The slow but strong Protoss have the easiest building method where only one unit needs to begin construction and then the building builds itself letting one unit set up all the buildings it can quickly then going back to work in seconds. Zerg on the other hand have their drones BECOME the building meaning each building costs one drone permanently making it the slowest and costliest method.
Impossible Creatures has 127,392 possible "characters", but these are simply specific combinations of 2 creatures, from a pool of 75. Of the creatures, many fit into a character tier:
Bombardier Beetles are the Squishy Wizard, but if combined with larger creatures, they can shoot poison up to 90 metres. Unlike most other ranged units, though, they don't have anything to fall back on if attacked at close range.
The Ken - a few creatures are described as with higher stats and . Mountain lions, for example, are slightly tougher and slower cheetahs. Panthers are slightly larger cheetahs, lions are larger panthers that get bonuses for attacking in a group, etc.
Game Breaker - Moose. To put it in perspective, nearly every army fields some sort of moose combo by level 5 (while mammoths and elephants are The Ken to moose, so they might be used). Those that don't use moose combo either have a unit meant to kill the more common moose-lobster or moose-gorilla hybrids, and it's not unheard of for an evenly matched player to send an army of normal moose to war against genetic mutants. Their Game Breaker status is only balanced by the fact that they cost a lot to summon, and it takes 10 minutes to reach the tech level to send out a moose hybrid even if you forgo base defense. But by this point, a single moose-lobster could take down most armies that a player would be using by the 10-minute mark.
Role Playing Game
While Pokémon is an RPG, the standard battle only has one mon per side at a time, and tends to have a cross between these and the ones for RPG.
Plus in the Meta Game, all Pokemon are sorted into several Character Tiers, with teams composed of Pokemon of the same tier being balanced against each other - and utterly destructive against those of lower tiers. Most commonly used tier ("over used") is actually a second tier, falling behind the "uber" tier, containing Purposefully Overpowered legendaries (and a couple of less dignified Game Breakers).
It's worth noting that not only are they based on stats, Tiers (at least in Gen IV) are worked out based on how resistant or weak an individual Mon is to Stealth Rock and their movepool. Pokemon like Charizard and Articuno, whilst still powerful, are considered some of the bottom of their tiers due to taking 50% damage from Stealth Rock. Although Pokemon like Moltres and Yanmega have the same degree of weakness to Rock-type attacks due to their typing, Moltres is considered as one of the top threats of its tier and it's one of the suspects (Pokemon discussed for a ban from its respective tier) of UU. Yanmega is already banned from UU. Pokemon like Ho-oh and Volcarona from Gen. V are in an entirely different class thanks to their nice movepools and appropriately-placed stats.
Fire Emblem games have most or all of the main character types, with the challenge being creating a team that has the best mix for the current level.
Though it's worth noting that certain characters can be gamebreakers. For example, in Path of Radiance, it is completely possible to solo the game with Ike, who can best be described as a Lightning Bruiser on steroids, alone.
Third Person Shooter
Monday Night Combat's six classes are pretty evenly distributed. The Assault is the Jack of All Stats, being mobile but not too mobile, powerful but not too powerful, etc. The Tank is the Mighty Glacier, existing to slowly plod his way through the level to the enemy base and then break stuff, which he does incredibly well. The Support is the Squishy Wizard, being a combination engineer and medic with some turret and bot buffs thrown in. The Assassin is the Fragile Speedster, having a frightening run speed and an absolutely brutal backstab attack. The Gunner is the Stone Wall, designed to shred enemy players that wander too close. Finally, the Sniper is the Glass Cannon, built around picking off enemies before they get into attacking range.
Non-video game examples:
Dungeons & Dragons: generally clerics are stone walls, fighters are almighty glaciers, rogues are fragile speedsters, and sorcerers and wizards are squishy wizards. Outside of the four "basic" classes barbarians and monks are lightning bruisers, paladins and rangers are magic knights, and bards and druids are jacks-of-all-stats (and masters of none) to different extents. There's quite a bit of room for customization in there though.
In terms of actual balance though this falls apart very quickly depending on the edition. In 3.5 the archetypes are quite well represented, but mean nothing because the Wizard, Archivist and Erudite classes exist relegating everything else to the role of porters. In 4th edition the archetypes were the basis for the class system's design, which lead to everything being equal in balance, but a loss in the diversity of classes being based on: Melee guy who chops, melee guy who gets chopped, Guy at Range With Weapon, Guy at Range With Magic, Healbot.
Truth in Television: Equipment and fighting styles in Roman gladiator matches were highly regulated to ensure an entertaining fight, and it was very common for a gladiator of one school to go against one of another—provided the two were compatible. For example, a common matchup had a retiarius—a Fragile Speedster armed with a trident and net—up against a secutor—a Mighty Glacier with a huge shield and small sword.