Sid Meier's Alpha Centauri/Special Ability

AAA Tracking
+100% defense vs air units.
 * Prerequisite: Advanced Military Algorithms
 * Cost: 1

Air Superiority
Allows a unit to attack air units in flight. Air units with Air Superiority gain a +100% combat bonus versus other air units but suffer a -50% combat penalty against ground and sea units.
 * Prerequisite: Doctrine: Air Power
 * Cost: 1

Algorithmic Enhancement
Improves probe team success rate and decreases probe attack energy costs. Also allows a probe team to attempt an attack on a base or unit under the Hunter-Seeker Algorithm or +3 PROBE, though at an extremely low success rate.
 * Prerequisite: Nanominiaturization
 * Cost: 1
 * Alien Crossfire only

Amphibious Pods
Allows ground units to attack sea bases, and allows ground units to attack from on board a sea-going transport. Also allows ground units to cross the gap between a friendly sea base and dry land without needing a transport in the base.
 * Prerequisite: Doctrine: Initiative
 * Cost: 1

Antigrav Struts
+1 movement rate for ground units, and ignore terrain movement penalties. An air unit with Antigrav Struts gains a movement rate increase equal to its reactor level.
 * Prerequisite: Graviton Theory
 * Cost: 1

Blink Displacer
Attacker ignores base defense bonuses.
 * Prerequisite: Matter Transmission
 * Cost: 1

Carrier Deck
Transport may carry air units.
 * Prerequisite: Nanometallurgy
 * Cost: 1

Clean Reactor
Unit does not require support from its home base. Not to be confused with the unit's Reactor, the Clean Reactor trait eliminates the cost of support. Note that probe and supply units inherently do not incur support costs, hence do not need this ability.
 * Prerequisite: Bio-Engineering
 * Cost: 2

Cloaking Device
Ground unit ignores zones of control (may move past enemy units without stopping).
 * Prerequisite: Frictionless Surfaces
 * Cost: 1

Comm Jammer
+50% defense vs. fast units (rover, hovertank).
 * Prerequisite: Advanced Subatomic Theory
 * Cost: Attack/Defense (rounded down, maximum 2)

Deep Pressure Hull
The ship operates underwater and will be hidden unless the square is entered by an enemy (doesn't work against computer players). May not be combined with the Carrier Deck ability.
 * Prerequisite: Nanometallurgy
 * Cost: 1

Deep Radar
Unit can see two squares away instead of one. Units with deep radar can see ONE square into the fungus, which is still an improvement, as without it one must actually enter said square to detect the unit.
 * Prerequisite: Advanced Military Algorithms
 * Cost: 0 for air or sea units, 1 for ground units

Dissociative Wave
Halves all positive combat bonuses (such as the +50% defense against fast units conferred by the Comm Jammer special ability).
 * Prerequisite: Centauri Psi
 * Cost: 2
 * Alien Crossfire only

Drop Pods
Allows a unit to make an Airdrop over a range of eight tiles, instantly moving from the tile of origin to the destination, provided that there are no air defenses near the destination tile, that the unit has not moved yet this turn, and that the unit is starting from a friendly base or airbase. Upon discovery of Applied Gravitonics (or upon completion of the Space Elevator, whichever comes first) any units with Drop Pods may instead make Orbital Insertions, which removes the eight-tile restriction. A unit that has made an Airdrop or Orbital Insertion may attack on the same turn, but will suffer a -50% combat penalty.
 * Prerequisite: Mind/Machine Interface
 * Cost: 2

Empath Song
+50% to psi offense.
 * Prerequisite: Centauri Empathy
 * Cost: 2

Fuel Nanocells
Adds +2 to an air unit's fuel supply, effectively increasing its range by 1.
 * Prerequisite: Matter Compression
 * Cost: 1

Fungicide Tanks
Formers remove fungus at double speed.
 * Prerequisite: Synthetic Fossil Fuels
 * Cost: 1

Heavy Artillery
Ground unit can make long range bombardment attacks from up to two squares distant. It is important to note that artillery units are incapable of attacking any other way.
 * Prerequisite: Polymorphic Software
 * Cost: Armor+Speed-2 (rounded down, maximum 2)

High Morale
Unit gains one automatic Morale upgrade, in addition to any conferred by the unit's respective facility (ie. Command Center, Naval Yard or Aerospace Complex).
 * Prerequisite: Intellectual Integrity
 * Cost: 1

Hypnotic Trance
+50% to psi defense. This is probably the most popular special ability in the game, perhaps rivaling Clean Reactor, putting defending land units on equal footing with attackers, and turning sea or air units into veritable psi fortresses.
 * Prerequisite: Secrets of the Human Brain
 * Cost: Attack/Defense (rounded down, maximum 2)

Marine Detachment
Allows an attacking unit to capture a severely damaged enemy sea unit. There can be bugs with this, such as capturing enemy naval forces in base squares. If it is a transport vessel, all land units defending the seabase are transferred over to your control, as if you had caught the transport at sea!
 * Prerequisite: Adaptive Doctrine
 * Cost: 1
 * Alien Crossfire only

Nerve Gas Pods
+50% attack bonus. Additionally, when attacking a city, kills half of the city's population (round up) if the attacking unit wins.
 * Prerequisite: High Energy Chemistry
 * Cost: 1

WARNING: using a unit equipped with this in combat against a human faction is considered a Simple Atrocity. That means if the UN charter is in effect, sanctions will be imposed upon you (nullifying commerce for at least 10 years), and regardless of the UN charter, the opponent on whom you used nerve gas will hate you forever. You can use this against the alien factions with no penalty.

Non-Lethal Methods
Unit counts as two for police purposes (suppressing two drones instead of one, and 3 if your police rating is +3 or higher!).
 * Prerequisite: Intellectual Integrity
 * Cost: 1

Polymorphic Encryption
Doubles the energy cost incurred by an enemy probe team attempt to subvert the unit.
 * Prerequisite: Pre-Sentient Algorithms
 * Cost: 1

Repair Bay
Transport acts as a bunker (units heal while on board).
 * Prerequisite: Nanometallurgy
 * Cost: 1

Soporific Gas Pods
Unit reduces Morale of non-native enemy units by two when attacking.
 * Prerequisite: Bioadaptive Resonance
 * Cost: 1
 * Alien Crossfire only

Super Former
All terraforming orders except for Remove/Plant Fungus are executed at double speed.
 * Prerequisite: Advanced Ecological Engineering
 * Cost: 1