You can have a lot of components. If there is an upper limit to how many you can have, it is set more by common sense than by game mechanics - that is to say, some components must be destroyed before the capship dies, so if you have too many, it'll take a hell of a lot of torps...
Anyway, from memory, these are the components you can have (and yes, you can have multiple components of the same type).
Bridge - requires torps to kill. If there is a bridge, it has to be destroyed to kill the ship.
Engine - requires torps to kill. If there is an engine, it has to be destroyed to kill the ship.
Tower 1 - this component was used on the Nephilim gate in Kilrah. Can be killed with any weapon (but the AI pilots are too dumb to notice this, so they'll only use torps). If there is a tower, it has to be destroyed to kill the ship.
Tower 2 - just like tower 1, but with a different name.
Tower 3 - [...]
Tower 4 - [...]
Tower 5 - [...]
Tower 6 - [...]
Tower 7 - [...]
Antenna - requires torps to kill. If still alive when the ship is destroyed, will blow up automatically.
Cargo - requires torps to kill. If still alive when the ship is destroyed, will blow up automatically.
Hangar - requires torps to kill. If still alive when the ship is destroyed, will blow up automatically. If destroyed in the player's base ship, will trigger the "You are unable to land" message.
Launcher - requires torps to kill. If still alive when the ship is destroyed, will blow up automatically. When the capship launches fighters, they come out of a launcher. If no launchers are available, nothing is launched. Presumably, it is the destruction of all Midway launcher components that causes that old WCP-crashes-on-mission-start bug.
Note that individual components cannot be renamed (so, if you have two bridge components, they'll both be called 'bridge'), but component types can be renamed (so, the above-mentioned two bridge components can also both be called 'lollipop', if you so desire). This makes the seven tower components quite useful, if you want to have lots of different component types. Never forget, however, that every single component will require at least one torpedo to be destroyed.