(EDIT: updated for 1.6.4)
Here is a list of the existing unique items in the game. There are several UU and UB. We also have some unique abilities (UA). Many of the special units are not really limited to one civ; they rely on a unique resource (UR) which is available to one civ but can be traded.
Atreides: Hawk Thopter, a UU replacement for Vulture Thopter with +1 move. Pilot School, a UB replacement of Aerie which gives more XP for starting thopter and hornet units.
Bene Gesserit: Sayyadina UU, teaches combat/drill promotions. Due to a bug this was not buildable until 1.6.3; no playtest feedback yet; passive effect which is hard to notice. Kwisatz Haderach UU, gives +25% strength in stack; moved from Atreides in 1.6.4, no feedback yet.
Bene Tleilax: Plague effect on combat result, and late game unit to provide ghola (clone) unit commanders with high experience. Playtest feedback is that plague spreads too much; no playtest feedback yet on the gholas.
Corrino: Imperial Trooper UU replaces heavy trooper; Laza Tiger UU replaces master guardsman; a HN unit intended to pick off isolated enemy units. Selamlik, UB of courthouse building which gives -50% war weariness. Several powerful UR melee units.
Ecaz: Elaccan Gladiator, UU of hardened bladesman; high strength, but automatically dies after any combat win or lose. Smuggler: has trade mission like Great Merchant but less powerful. Smuggler's Haven: two additional landing stages. Sculptor's Garden: UB of Mushtamel; +1 trade route.
Fremen: All initial units, and some later foot units, start with double speed desert movement. Several powerful melee UR units.
Harkonnen: Devastator Tank UU of Heavy Scorpion. Slave Pit, UB of courthouse which has no real effect since slavery "whip" is temporarily removed. Inkvine Regiment UU of Heavy Trooper. Can generate slave units on combat victory.
Ix: four walker UR units; playtest feedback is that they should be strengthened a little, spread out better in the tech tree, and also given a national limit of 10. Three UB which are variants of the late game automated factory and research center; these use thinking machines, and the Ixian variant avoids the happiness penalty. Strong disagreement about overlap between Ixian buildings and Technocracy.
Ordos: spy units gain 1 XP per turn. Trike, UU of Quad with +1 movement.