Rigs
Rigs are permanent ship modifications that fit into the rigging slots of a ship. Once fit, they must be destroyed in order to be removed, unlike regular modules. They don't have powergrid or CPU fitting requirements, but most have some other drawback associated with them. These penalties are reduced by training more levels in the associated rigging skill: the amount of speed reduction caused by armor rigs, for example, is lessened (though never completely eliminated) by your Armor Rigging skill.
Each rig requires calibration, a rig specific fitting resource. All ships have 400 calibration, except for pirate faction ships which have 350. Rig calibration requirements range from 50 to 200, with tech 2 variants requiring 50% calibration than their tech 1 equivalents.
Rigs are made from salvaged material.
Armor
Unless otherwise noted, fitting these rigs will reduce your ship's maximum velocity.
Nano Pump: Increases the amount an armor repair repairs. Increases armor repairer powergrid requirements.
Nanobot Accelerator: Reduces the armor repair cycle time. Increases armor repairer powergrid requirements.
Remote Repair Augmentor: Reduces the capacitor need for a remote repair.
Resistance Pumps: Increase armor resistances (each damage type has its own rig).
Transverse Bulkhead: Increase total hull hit points by a percentage. Decreases cargo capacity.
Trimark Armor Pump: Increases total armor of a ship by a percentage, without a stacking penalty.
Astronautic
Unless otherwise noted, fitting these rigs will reduce the amount of armor on your ship.
Auxiliary Thruster: Increases maximum velocity.
Cargohold Optimization: Increases cargo capacity.
Dynamic Fuel Valve: Decreases the amount of capacitor used by afterburners and microwarpdrives.
Engine Thermal Shielding: Increases the duration of afterburner or microwarpdrive cycles.
Higgs Anchor: Increase mass and agility while greatly reducing maximum velocity. Reduces warp velocity. Only one can be fitted.
Hyperspatial Velocity Optimizer: Increases your maximum warp velocity. Increases signature radius.
Low Friction Nozzle Joints: Increases agility.
Polycarbon Engine Housing: Increases maximum velocity and speed.
Warp Core Optimizer: Reduces the capacitor needs for warping. Increases signature radius.
Drone
Fitting these rigs will reduce your ship's CPU capacity.
Control Range Augmentor: Increases the range at which you can control drones.
Durability Enhancer: Increases the HP of drones.
Mining Augmentor: Increases the yield of mining drones and decreases cycle time for ice harvesting drones.
Repair Augmentor: Increases the repair of repair drones.
Scope Chip: Increases the optimal range of drones.
Speed Augmentor: Increases the speed of drones.
Sentry Damage Augmenor: Increases the damage of sentry drones.
Stasis Drone Augmentor: Increases stasis drones' factor of velocity decrease.
Electronics superiority
Fitting these rigs will reduce the amount of shields on your ship.
Inverted Signal Field Generator: Increases the effectiveness of remote sensor dampeners.
Particle Dispersion Augmentor: Increases the strength of ECM modules.
Particle Dispersion Projector: Increases the range of ECM modules.
Signal Disruption Amplifier: Decreases the capacitor need for ECM modules.
Targeting Systems Stabilizer: Decreases the targeting delay after uncloaking.
Tracking Diagnostic Subroutines: Increases the effectiveness of tracking disruptors.
Engineering
These modules have no penalty.
Ancillary Current Router: Increases ship's powergrid.
Capacitor Control Circuit: Increases ship's capacitor recharge rate.
Command Processor: Increase the number of Command Burst modules that can be equipped to a command-capable ship.
Egress Port Maximizer: Decreases the capacitor use of all energy emission modules.
Liquid Cooled Electronics: Reduces the CPU needs of modules that require the electronics upgrade skill.
Powergrid Subroutine Maximizer: Decreases the CPU need for all power upgrade modules.
Processor Overclocking Unit: Increases the base amount of CPU of your ship.
Semiconductor Memory Cell: Increases a ship's total capacitor.
Missile launcher
Fitting these rigs will increase the amount of CPU required by any missile launchers fitted to your ship.
Bay Loading Accelerator: Increases the rate of fire of launchers.
Hydraulic Bay Thrusters: Increases missile velocity.
Rocket Fuel Cache Partition: Increases missile flight time.
Warhead Calefaction Catalyst: Increases missile damage.
Warhead Flare Catalyst: Increases missile explosion velocity.
Warhead Rigor Catalyst: Decreases the explosion radius of missiles.
Resource procurement
These rigs have no penalty.
Ice Harvester Accelerator: Reduces the duration of ice harvester cycles. Available only in medium size.
Mercoxit Mining Crystal Optimization: Increase the yield modifier of modules using Mercoxit mining crystals. Available only in medium size.
Salvage Tackle: Increases the chance to salvage successfully. Has a max velocity penalty mitigated by Armor Rigging skill.
Scanning
These rigs have no penalty.
Emission Scope: Increases the success chance of analyzer modules.
Gravity Capacitor: Increases the strength of scan probes.
Memetic Algorithm Bank: Increases the success chance of hacking modules.
Signal Focusing Kit: Increases the speed of scanners (cargo, ship, and survey scanners).
Shield
Fitting these rigs will increase your ship's signature radius.
Screen Reinforcers: Increase your resistance to a particular type of damage.
Core Defense Capacitor Safeguard: Decreases the cap used by modules that require the shield operations skill.
Core Defense Charger Economizer: Decreases powergrid use of shield upgrade modules.
Core Defense Field Extender: Increases shield capacity.
Core Defense Field Purger: Increases shield recharge rate.
Core Defense Operation Solidifier: Decreases the cycle time for shield boosters.
Targeting
Fitting these rigs will reduce the amount of shields on your ship.
Ionic Field Projector: Increases your maximum targeting range.
Targeting System Subcontroller: Increases your targeting speed.
Turret weapons
Fitting these rigs will increase the amount of power grid required by any turrets fitted to your ship. There are variations for each type of turret, ie hybrid, energy, and projectile.
Algid Energy Administrations Unit: Decreases turret CPU needs.
Ambit Extension: Increases turret accuracy falloff.
Burst Aerator: Increases turret rate of fire.
Collision Accelerator: Increases turret damage.
Discharge Elutriation: Decreases turret capacitor use. (Note that there is no Discharge Elutriation rig for projectile turrets, because they use no capacitor in the first place.)
Locus Coordination: Increases turret optimal range.
Metastasis Adjuster: Increases turret tracking speed.