The black, "tough-guy" gamer who just wants to kill things, and seek "ULTIMATE POWER!" (along with his white, Frat-boy counterparts). AKA The "Hack'n'Slasher".
The well-dressed, well-to-do "Preppie Gamer".
The general, average, run-of-the-mill "Normal Gamer", AKA "Most of Us". You can't tell'em from the average Man-in-the-Streets, although they tend to be a bit more academic, well-read, and use words like "Wield" and "dweomer" that aren't in most dictionaries or Lexicons (Oops! See?)
The Punk-rocker Bard.
The quiet, introverted, "Social Gamer" who doesn't know the rules, or care to learn them, he just plays because his friends do.
The "Girlfriend Gamer" who games socially only because her boyfriend does, and she just wants to spend more time with him (basically, a variant of the above).
The 'Mancer. Is in it for the fantastic elements. In D&D, always plays a Wizard/Sorcerer. In Sci-Fi, always plays the highest Tech PC available.
The Strategist - Enjoys solving the problems that the GM throws at him, usually with the smallest amount of equipment available, whether by spell, might & main, hard work, or whatever. Problem-solvers.
Roleplayers - While all gamers are RPers, more or less, RPers focus on playing their character's personality, more than anything else. Not so interested in "ULTIMATE POWER" as WHY their PC would want it, and what they'd do with it, if they had it! They'd rather talk to a Dragon than kill one.
The Generalist - Doesn't have to be the best at anything, but always has to at least have a shot at doing anything in the game. Spends a lot of time helping, planning, aiding another, and never really Min-Maxes their PC to be the best at anything, but instead puts a few skill points/Feats into this and that area... His/Her PC can probably pick a pocket, pick a lock, cast a few spells, sling a sword, and organize the other Co-operative PCs into a functioning party, even if no one of them can overcomes an obstacle by themselves.
The Planner - Doesn't think so well on their feet, but plans well, in advance. Pulls out the acid to perma-slay the Troll when no one else has anything. Whips out the Glow-stick when the Anti-magic sphere goes off, and all the Everburning Torches wink out. Has the only extra set of lockpicks in the party when the Rogue breaks hers (and they're Masterwork, too!)
The Improvisor - The Planner's counterpart. Never plans for anything, but is mentally "Quick on his Feet", and can come up with the fastest, often best, solution at the spur of the moment. Is often a Strategist, as well.
The Brooding Loner - Always attempts to operate alone, until beaten down and in need of healing, or (s)he faces something their PC can't handle, alone. Then they return to the party.
There are many more, surely.