Note: The term "air cover", when dealing with space-based combat roles, is a holdover from the 20th Century. Modern military analysts often use the term "space cover", but this has not taken hold in common usage as expected.
Carrier - Provide air cover through the carrier's fighter wing, with a secondary role as a flagship of a fleet or task force. At least half of the space on board a carrier is dedicated to maintaining the flight wing.
Battleship - Serve as an artillery platform against surface installations, space stations, and other larger vessels (cruisers, battleships, and carriers). Also has a secondary role, alongside the dedicated carrier, as the flagship of a fleet or task force. Most of the free space inside the battleship is dedicated to ammunition for the weapons.
Cruiser - Serve as an escort for the larger carriers and battleships; act as flagships for the smaller task forces; and provide strike capability against other ships and space stations through its guns and missiles.
Strike Carrier - Provide air cover through the carrier's flight wing; serve as an escort for the larger carriers and battleships; act as a flagship for smaller task forces; and provide strike capability against other ships and space stations through its guns, missiles, and fighters. Roughly one third of the ship is dedicated to the flight wing, another third to the weapons systems.
Escort Carrier - Provide air cover for battleships, cruisers and bulk freighters through the carrier's flight wing. Two thirds of the escort carrier's space is used to support the flight wing.
Destroyer - Serve as an escort for the cruisers and strike carriers; act as point defense around carriers, battleships, space stations, and bulk freighters; and provide additional firepower against other ships.
Marine Transport - Serve as a home base for marine contingents, housing the marines, their equipment, their dropships, and their assault shuttles. Analogous to today's Amphibious Landing Ships. Many Marine Transports are converted Strike Carriers or Escort Carriers, others are designed with the intent of being Marine Transports.
Frigate - Serve as an escort for the cruisers, strike carriers, and destroyers; and provide point defense around all larger ships.
Patrol Boat - Provide in-system patrols for space stations, carriers, and strike carriers; provide an additional layer of point-defense for cruisers and larger; and escort for freighters. Almost never FTL-capable, and often deployed in squadrons. FTL-capable patrol boats are often called Corvettes, although that classification is also reserved for any ship that falls between the Frigate and Patrol Boat in size and purpose.
Racker - Transport fighters into a combat zone and release them; provide rearming for fighters under combat conditions, especially when a larger mothership is not feasable.
Assault Shuttle - Provide marines with the means for conducting boarding parties during both the insertion and extraction phases; and protecting the marines while en route to their target.
Dropship - Provide infantry, mechanized infantry, and armored forces with the means to make insertions and extractions into and out of planetary combat zones. Analogous to today's Amphibious Landing Craft.
Interceptors - Provide fast, long-range air cover in order to stop approaching enemy fighters and bombers as fast as possible.
Space Superiority Fighters - Elimination of enemy air cover; and provide escort for the bombers, dropships, and assault shuttles.
Attack Fighters - Elimination of enemy frigates, destroyers, and cargo craft; and eliminate weapon emplacements on enemy carriers, cruisers, strike carriers, battleships, and space stations.
Multi-Role Fighters - Elimination of enemy air cover, frigates, destroyers, and cargo craft; elimination of weapon emplacements on enemy carriers, cruisers, strike carriers, battleships, and space stations; and provide escort for the bombers, dropships, and assault shuttles.
Bombers - Elimination of enemy carriers, battleships, cruisers, strike carriers, bulk freighters, and space stations. Some bombers have been outfitted with grappling lines to provide Search and Rescue functions.
SWACS Craft - "SWACS" stands for Spaceborne Warning And Control Systems. Provide identification of friendly, hostile, and neutral craft prior to and during combat conditions; extend the effective range of fleet sensors; and to scout nearby systems. Some SWACS craft have been outfitted with grappling lines to provide Search and Rescue functions.
Bulk Freighters - Transportation of goods from system to system, usually from space station to space station or station to ship, as very few bulk freighters can make planetary landings. A number of bulk freighters are actually passenger liners.
Light Freighters - Transportation of goods between planets, stations, ships, and systems. A number are capable of search and rescue, and are often used by pirates and smugglers as blockade runners, or by couriers, messenger services, and slavers.
Colony Ship - Provide transportation of families and personal items, as well as the necessary facilities, to generate a self-sufficient colony.
Colony Ship: Generation - Provide long-term living space for a colony planet; usually travels at sublight speeds. May take thousands of years to reach the colony planet. Generally completely self-sufficient.
Colony Ship: Sleeper - Provide cryogenic sleeping capsules for colonists while en route to a colony planet; depending on technology levels, can travel at sublight or very slow FTL speeds.
Tenders - Provide medical assistance; additional living space; additional cargo space, ammunition, or fuel; or any other additional non-combat function necessary.