Giving my own thoughts, some of them already mentioned but with different effects or names:
Culture War: Knocks off small amount of Culture based off difference between total culture of both civs as well as total culture in the city.
Industrial Sabotage: Temporarily decreases health and lowers production.
Industrial Espionage: Siphons a small number of tech points for a random tech unresearched by the spying civ but known to the target civ each turn the spy remains in the city.
Sabotage Monument: Destroys one culture-producing building and an amount of small amount of culture (varying directly by what the building produced). Target civ "recoups" a small amount of cost in gold.
Legislative Sabotage: Stops all progress on current project for a small number of turns (project can still be changed or bought).
Sabotage Project (currently just Sabotage): Destroy 1/2 of progress on current project.
Bribe Officials: Diplomatic bonus with civ; target civ gets a small "cut" of the bribe.
Propaganda: Diplomatic malus between target civ and random third civ that spying civ has a poor relationship with.
Criminal Contacts: Siphons a small amount of gold each turn to the spying civ.
Black Market: Spying civ receives access to a random resource of target civ, temporarily, with a preference for strategic resources (think Uranium).
Smuggle Narcotics: Decreases health in target city, Spying civ receives small "cut" of profits in return (with the potential to make a net profit, say a 5% chance).
Plant Mole: Target unit gains "Suspicious" promotion, and provides line of sight for the spying civ so long as the original spy lives.
Terrorism-- not sure if these require a seperate unit or not, but would all definitely need some sort of diplomatic penalty (and/or War Weariness) if the originating civ is made known. It is also questionable whether or not some of the above Sabotage missions need a big penalty or not, or whether some of the below shouldn't get as big a penalty.
Chemical Bomb (Terrorism): May destroy a building, may remove 1 population, small temporary health penalty.
Biological Attack (Terrorism): Large temporary health penalty, may remove 1 population.
Arm Insurgents (Terrorism, must have at least 1

in excess of

): City acts as if it has undergone a riot on behalf of the spying civ, damaging units and temporarily halting production.
Assassination (Terrorism): Temporary happiness penalty, removes one permanent specialist.
Smuggle Nuclear Device (Terrorism): City acts as if it has experienced a Meltdown.
As for 'buying' units: I don't care for the idea, and I don't really think there's a good way to implement it. At best, I think it should be possible to cause a unit to disband if it isn't in a stack, but not defect to your side, and it should cost a great deal (exponentially higher for more experienced units) to try to pull it off.