Games that uses a Character Class System are likely to use classes that are at least somewhat familiar. This is for several reasons. One is that these classes fill useful roles in battle, so they keep reappearing in an example of convergent design. Another is the fact that designers generally want to make switching to their system easy, so more people will do it; when the classes are already somewhat recognizable, that lowers the barrier to entry for a new player trying to pick up the game for the first time. See Character Class System for a discussion of classes in general, and Fighter, Mage, Thief for a common tripartite division. This is obviously not meant to be an exhaustive list, but merely to hit the highlights; please keep this in mind. In addition, this is a genre-neutral list — Character Class Systems are primarily used by RPGs, but show up in everything from FPSes to Strategy Games these days, and this list is meant to reflect that without bias toward any particular genre.
WarriorMay also be called "fighter", "soldier", or some other variation of the theme "guy who fights". Their job is to hit the frontlines and engage in direct combat with the enemy. They tend to be something of a Jack of All Stats, though they usually lean toward Mighty Glacier as well, being a bit tougher and stronger than usual at the cost of being slightly slower than average. Though they usually specialize in melee combat, many variants can be quite good at ranged combat as well. The "default" option for many games, they're usually the simplest class to play.
RogueAlso "scout" or "thief", they emphasize speed and/or stealth above all else. This makes them ideal for Hit-and-Run Tactics, given that they're good at both ambushing the enemy and avoiding fights they don't like. Typically a Fragile Speedster, they're usually not sturdy or powerful enough to carry things on their own, but are none the less valuable for weakening and disrupting the enemy.
RangerAlso "archer", "gunner", or "sniper", they specialize in powerful long-range attacks. They're generally a Glass Cannon, capable of dealing lots of damage to a single target from a safe distance, but aren't very good at defending themselves, especially in melee combat (assuming that they're even capable of melee combat in the first place). Best used to take out high-value or defense-heavy targets while being sure to keep their beefier teammates between them and the enemy.
SupportAlso "healer" or "buffer", they improve their allies' ability to fight without adding much on their own. They may aid teammates by healing them to keep them alive longer, by offering bonuses to allies, or by inflicting penalties on enemies. Either way, as a variety of Squishy Wizard, a support class by himself is generally easy prey. Requires more teamwork than most classes, which can be frustrating on both sides; bad support can bring down a good team, but a team that doesn't protect their support is equally annoying.
NukerThe class with the most different names and hardest to define, their singular uniting characteristic is the ability to mow down foes. Whether they're a mage casting fireballs or a weapons specialist with a heavy machine gun, they can cover lots of ground with area of effect attacks, rapid fire, or both. This makes them especially deadly against large numbers of individually weak enemies. They're usually either a Glass Cannon unable to take hits or a ponderously slow Mighty Glacier. In the right circumstances they can wipe out hordes of opponents, but if caught in a bad spot they'll go down like a pile of bricks. See also PVP Balanced, An Adventurer Is You, Competitive Balance, and Fantasy Character Classes.