I have seen relatively few unique character specialties. The ones I have seen, in alphabetical order, are:
Artillery and Heavy Weapons
* This is the magic-user with a fireball or the space marine with a Fusion-Gun-Man-Portable-15. Weapons such as the M-79 grenade launcher blur the line between this specialty and small-arms ranged combat.
Artistry/Performance/Public Speaking
* This is a person who can impress a whole crowd at once. He or she might be an orator, an actor, a showman, a fashion runway model, a musician, etc. Note that this person might lack one-on-one social skills.
Civilized Businessperson
* This is the merchant, the lawyer, the cargo document manager who is only necessary when the adventure involves fairly civilized business interactions. Player character thieves whose only contacts are fences are participating in this role.
Connections and Contacts
* This is the person who knows lots of useful people. If the party includes Bertie-Wooster-style noblemen, the person may be useless, penniless, and brainless -- but still valuable due to his social standing. In modern urban adventures, this is the guy who knows arms dealers, crooked cops, etc.
Combat, Ranged
* This person does combat at a distance, generally including very-long-range weapons and grenade-like weapons. Sniper rifles, longbows, possibly even magical rays fit into this role.
Combat, Hand to Hand
* This person does close-quarters battle. Usually he or she is armed and armored, but fist-fighters are included. Depending on the system, this can have a great deal of overlap with ranged combat, e.g. when a phalanx of infantry decides to hurl its spears and draw its swords, or when a Viet Cong runs out of rifle ammo and charges with his attached bayonet.
Craftsmanship/Repair/Invention/Resource Extraction
* This can include inventors, farmers and miners, but usually these specialists are concerned with making and repairing tools and objects.
Exotic Movement/Acrobatics
* This includes the ever-popular acrobatic thief and the high-jumping martial artist.
Familiars/Followers/Personal Bodyguards
* This is possibly the specialty most hated by referees/DMs/GMs. The character who has a retinue of personal bodyguards, whether they are familiars, charmed wild animals, robots, or zombies, frequently can avoid many risks. This specialist is sometimes called a "pet owner" and sometimes can be handled more easily by computer games than by human DMs. This can be an excellent choice for one-on-one tabletop games, however, when there are not enough human players to fill an ordinary party. Some D&D players might consider that wizards controlling summoned monsters are using this niche for short periods of time.
Medic/Healer
* This person heals player characters, and can usually heal non-player characters as well.
Owner of Property/Castles/Starships
* In settings with stable and widely respected notions of property, a character can be important simply by owning a piece of capital useful for adventurers, such as a castle, a starship, a sailing ship, etc.
Pilot/Transportation Technician
* If the party needs specialized vehicles, it may need one or more player character pilots. In fantasy settings, a wizard who transports the entire party by planar gates or teleportation is basically filling this role.
Social Interaction(Training, Diplomacy, Seduction, Interviews)
* This is a person skilled at dealing with one-on-one and small-group social interactions. The private detective, the diplomat, the fencing teacher, and the seducer all fit this role.
Stealth/In-person Recon
* This person gathers information by personally infiltrating an area of interest. Lock-picking, trap detection, and other means of defeating guards and surveillance systems are part of this role.
Library Research/Divination/Lab Analysis/Remote Recon
* This person gathers information from a secure location, usually well out of danger. The wizard casting divination spells, the computer hacker sitting in an armored van and watching screens, the bookworm in the library and the scientist in the starship's research lab all fit this mold.
So, in all, I think I can only identify fifteen niches. In most cases, a tabletop group of fifteen players and a referee is impractically large. Also many niches do not mix well together. If only one player is in the lab (or on the Internet), doing research, the rest of the party often gets bored.
The norm is for each character to have multiple roles. In D&D, thieves often cover Stealth and Exotic Movement. In Traveller, the Owner of the Starship is often also the Pilot and Civilized Businessperson. In Shadowrun, cyberware users often fill multiple roles requiring cyberware, such as Pilot and Remote Recon.
Very few adventures are designed for odd roles, although parties with odd specialties are perhaps my biggest motivation for tabletop gaming. Very few games have farmers -- although I know of a Rolemaster campaign where a farmer with the backing of the goddess of agriculture was the most powerful party member -- so if you can actually get a farmer to survive the adventuring life, chances are good that he (or she) will have stories worth telling.
Artillery and Heavy Weapons
* This is the magic-user with a fireball or the space marine with a Fusion-Gun-Man-Portable-15. Weapons such as the M-79 grenade launcher blur the line between this specialty and small-arms ranged combat.
Artistry/Performance/Public Speaking
* This is a person who can impress a whole crowd at once. He or she might be an orator, an actor, a showman, a fashion runway model, a musician, etc. Note that this person might lack one-on-one social skills.
Civilized Businessperson
* This is the merchant, the lawyer, the cargo document manager who is only necessary when the adventure involves fairly civilized business interactions. Player character thieves whose only contacts are fences are participating in this role.
Connections and Contacts
* This is the person who knows lots of useful people. If the party includes Bertie-Wooster-style noblemen, the person may be useless, penniless, and brainless -- but still valuable due to his social standing. In modern urban adventures, this is the guy who knows arms dealers, crooked cops, etc.
Combat, Ranged
* This person does combat at a distance, generally including very-long-range weapons and grenade-like weapons. Sniper rifles, longbows, possibly even magical rays fit into this role.
Combat, Hand to Hand
* This person does close-quarters battle. Usually he or she is armed and armored, but fist-fighters are included. Depending on the system, this can have a great deal of overlap with ranged combat, e.g. when a phalanx of infantry decides to hurl its spears and draw its swords, or when a Viet Cong runs out of rifle ammo and charges with his attached bayonet.
Craftsmanship/Repair/Invention/Resource Extraction
* This can include inventors, farmers and miners, but usually these specialists are concerned with making and repairing tools and objects.
Exotic Movement/Acrobatics
* This includes the ever-popular acrobatic thief and the high-jumping martial artist.
Familiars/Followers/Personal Bodyguards
* This is possibly the specialty most hated by referees/DMs/GMs. The character who has a retinue of personal bodyguards, whether they are familiars, charmed wild animals, robots, or zombies, frequently can avoid many risks. This specialist is sometimes called a "pet owner" and sometimes can be handled more easily by computer games than by human DMs. This can be an excellent choice for one-on-one tabletop games, however, when there are not enough human players to fill an ordinary party. Some D&D players might consider that wizards controlling summoned monsters are using this niche for short periods of time.
Medic/Healer
* This person heals player characters, and can usually heal non-player characters as well.
Owner of Property/Castles/Starships
* In settings with stable and widely respected notions of property, a character can be important simply by owning a piece of capital useful for adventurers, such as a castle, a starship, a sailing ship, etc.
Pilot/Transportation Technician
* If the party needs specialized vehicles, it may need one or more player character pilots. In fantasy settings, a wizard who transports the entire party by planar gates or teleportation is basically filling this role.
Social Interaction(Training, Diplomacy, Seduction, Interviews)
* This is a person skilled at dealing with one-on-one and small-group social interactions. The private detective, the diplomat, the fencing teacher, and the seducer all fit this role.
Stealth/In-person Recon
* This person gathers information by personally infiltrating an area of interest. Lock-picking, trap detection, and other means of defeating guards and surveillance systems are part of this role.
Library Research/Divination/Lab Analysis/Remote Recon
* This person gathers information from a secure location, usually well out of danger. The wizard casting divination spells, the computer hacker sitting in an armored van and watching screens, the bookworm in the library and the scientist in the starship's research lab all fit this mold.
So, in all, I think I can only identify fifteen niches. In most cases, a tabletop group of fifteen players and a referee is impractically large. Also many niches do not mix well together. If only one player is in the lab (or on the Internet), doing research, the rest of the party often gets bored.
The norm is for each character to have multiple roles. In D&D, thieves often cover Stealth and Exotic Movement. In Traveller, the Owner of the Starship is often also the Pilot and Civilized Businessperson. In Shadowrun, cyberware users often fill multiple roles requiring cyberware, such as Pilot and Remote Recon.
Very few adventures are designed for odd roles, although parties with odd specialties are perhaps my biggest motivation for tabletop gaming. Very few games have farmers -- although I know of a Rolemaster campaign where a farmer with the backing of the goddess of agriculture was the most powerful party member -- so if you can actually get a farmer to survive the adventuring life, chances are good that he (or she) will have stories worth telling.