One of the ongoing discussions in any game with an active community is usually what character/class is over or underpowered. This usually takes the form of one group saying something is overpowered, another group pointing out how they totally aren't overpowered, and another group that either makes fun of the whole thing or says that another thing is what is really overpowered.
However, overpowered characters are not necessarily a bad thing. Most of my favorite games have them. Perhaps that says more about me than it does the games, but nevertheless...allow me to present my favorites.
Game: Castlevania: Symphony of the Night
Why??: Alucard is Dracula's son. Therefore, he has all kinds of awesome-ness already going for me. Specifically to Symphony of the Night, it means that, almost from the minute you start the game, you're a walking death machine. Once you start to get better equipment and spells, the game becomes a cakewalk. In fact, this entry in the Castlevania series is notoriously easy, especially if you abuse things like the Shield Rod + Alucard Shield combo, the spell that drains the life of enemies, or the Crissaegrim sword. You might immediately say "Well, Alucard is the only playable character in the game, so does he count as overpowered?!" but you forget that you can unlock Richter Belmont and, depending on the version you're playing, Maria. Richter is a bit more challenging, while Maria is awkward and lame. So, yeah, Alucard is stupidly powerful.
Who??: Peter the Phoenix
Game: Shining Force II
Why??: When you first get Peter in your party, he looks like he does above and is controlled by the computer. Once you see him in action during a battle, though, you'll quickly learn why Peter is considered the best character in the game. Or at least the cheapest. Unlike some of the other characters in the Shining Force series, who start out horrible but with a lot of work become unstoppable, Peter is immediately awesome. After he's promoted and he starts looking more like an Aztec bird god instead of a retarded muppet, he becomes even better. Not only does Peter automatically resurrect himself so you don't have to pay money after battles to get him back, but he has gobs of attack, speed, and HP. Also, in the game's story, he permanently joins your party on the order of a God. Sweet.
Who??: Orlandu a.k.a. T.G. Cid
Game: Final Fantasy Tactics
Why??: Orlandu is one of the earliest known times where people began to use terms like 'overpowered.' Though he joins your party well into the game, he comes with the All SwordSkill ability set, meaning he can use ALL of the awesome Sword Skill attacks in the game. You know, the ones that are way too powerful and awesome. Not only that, he comes with the Excalibur sword, which casts Haste on any character wielding it. So he gets twice as many turns as your other characters, and he has some of the best unique attacks. Assuming you twink him out with some of the abilities from the game's other unbalanced classes (hello, Dual Wield from Ninjas) he becomes, you guessed it, even more powerful. Obligatory Note: T.G. Cid stands for "Thunder God Cid."
Game: World of Warcraft
Why??: Warlocks are a contentious subject in WoW. They have been considered overpowered since the release of the game, and while they aren't the "automatic win" that most of the other characters I'm talking about are, they still are pretty bad. WoW is a game where most classes have a specific role, or two, to play. Warlocks can seemingly do everything in the game at once, even if some of those roles are better done by other classes. Just for the sake of argument: they can DPS with awesome spells, DOT with awesome curses, resurrect healers, create items that quickly heal other players, breathe underwater with a spell, crowd control with Banish or Fear or Enslave, get their mounts and epic mounts for free (requires doing involved quest chains, but still), tank via certain pets (Felguard says "hi!!"), summon other players, siphon mana or health from enemies...
The most telling thing about Warlocks is that, for a class that can only wear cloth armor, they dominate in PvP. This is because they can max out their Stamina--thus getting a nearly bottomless reservoir of HP--and use an ability that quickly converts HP into mana, effectively giving them infinite MP for spells and making them nearly unkillable. Combined with a healer class like Paladin or Priest, in 2 v 2 matches they are gods. Combined with Shadow Priests in PvE questing, instanced dungeons, or raids, their combined Shadow spells and Shadow resistance lowering effects make them great in every situation. Whew.
Why??: The first Diablo is embarrassingly unbalanced to the side of Sorcerers. Of the three available classes, they become unstoppable whirling death by game's end due to their array of spells and Mana Shield. Basically, Mana Shield causes you to take damage from your MP instead of HP. At the same time, you can spam Guardian (which summons three-headed dragon dealies to shoot at enemies) and Apocalypse (which is the big, end-game nuke spell of the game) to roll over your enemies with ease. Sorcerers are the definition of overpowered, though the early-to-mid game can be rough as it is for every caster class in most Western style RPGs. Speaking of which...
Game: Icewind Dale: Heart of Winter
Why??: I chose this one for last because it's one of the more interesting examples of the changes an expansion can bring to a seemingly set-in-stone game. The thing is, I like music a lot, but in the context of RPGs, Bards are unspeakably lame. This was especially true in the D&D games that Bioware/Black Isle developed in the late 90s/early 00s. However, with the Heart of Winter expansion pack for the dungeon hacky Icewind Dale, Bards became arguably the best class in the game, with the exception of Druids. Bards are kind of like the Warlocks of Icewind Dale: they do a lot of things and a good number of those they do well. Bards can pickpocket like Thieves, cast spells like Mages, get buffs in the form of songs, can identify items with their high Lore rating (an awesome skill that most people take for granted), get some great Bard-only items, can do certain quest things that other characters can't (in the first town, they can sing to a ghost for extra experience), and, possibly, could tank. I never bothered with the latter, though. Maybe 'overpowered' is too strong a word, but the Heart of Winter changes made the Bard one of the best classes in the game. With the final song (which they learn at a measly level 11) they become an essential part of your party.