Features

Adds equipment grids to vehicles in a sensible manner (so no more exoskeleton legs in cars and trains and ships and planes)
Instead adds one vehicle-specific equipment for the movement speed boost.
No changes made to spidertron entities, as they are clearly made of legs, and uses exoskeleton legs in the recipe.
If you wish to modify the grid sizes, use the addon mod Vehicle Equipment Grids Customizer
Otherwise, the default values will be used as listed below:
Tank: 9x6 (almost every other equipment grid is balanced around this, which is the vanilla grid size for this vehicle)
Car: 7x4 (non-militaristic, unlocked much earlier, with two fewer science pack types, requiring much fewer resources, and no red circuits)
Basic Trains: 9x4 (includes locomotive, cargo wagon, and fluid wagon, smaller because they are each limited in the type of equipment they can use)
Artillery Trains: 9x6 (much further along in the tech tree, requiring 5 science packs compared to just 2, but is also quite limited in usable equipment)

Fully Compatible Equipment Mods:

Bob's Personal Equipment and Bob's Vehicle Equipment: Adds vehicle-specific equipment that will apply to all vehicles added by other mods, while also preventing personal equipment from being used in those vehicles.
Radar Equipment: Adds radar functionality to vehicles when equipped so they can be driven remotely in areas without coverage.
Gun Equipment: Adds portable automatic weaponry (similar to personal laser defense) to vehicles when equipped, using ammo from the vehicle's inventory, with auto-reloading capability.
SMG Equipment: Similar to the Gun Equipment mod, except this version does not require ammo, and has a more expensive up-front recipe cost.
Microwave Transmission: Adds microwave transmission towers which can wirelessly charge batteries in vehicle equipment grids, via microwave receiver equipment.
Modular Charge Packs: Adds reusable battery packs that requiring charging via physical charging station, before being placed in equipment grids.
Schall Primary Battery: By contrast, adds cheap, early-game, one-time-use battery equipment.
Lightning Collector Equipment: Adds a portable lightning collector, protecting vehicles from taking damage, and simultaneously charging batteries, from lightning strikes.
Aircraft (Space Age Update): The aircraft-exclusive equipment (afterburner and shields) become available to all vehicles listed in the aircraft section below.
Extended Vanilla: Personal Equipment: Backpacks increase vehicle inventory size when equipped (also acts as belt immunity). Assembling unit equipment has no effect on vehicles, so they have been blacklisted from being placed in their grids. All other upgraded equipments function as normal.
Any other mod that simply adds upgraded versions of pre-existing equipment like batteries, reactors, solar panels, laser defense, etc. should just work in vehicle equipment grids as normal.

Fully Compatible Grounded Vehicle Mods:

AAI Vehicles: Chaingunner: 5x4 (very cheap early-game vehicle)
AAI Vehicles: Flame Tumbler: 7x4 (since it is basically a car)
AAI Vehicles: Miner: 5x4, 7x4, 9x4, 9x6, 9x8 (starts small, increases by tier)
AAI Vehicles: Hauler: 9x4 (big bulky support vehicle)
AAI Vehicles: Warden: 9x6 (bigger bulky support vehicle)
AAI Vehicles: Flame Tank: 9x4 (tank in name only, doesn't require blue science or red circuits)
AAI Vehicles: Laser Tank: 11x6 (actually stronger than tank, and more expensive)
Tesla Tank: 11x6 (similar to laser tank, stronger and more expensive than vanilla tank)
Hovercrafts: [default 7x6] (user-defined by Hovercrafts mod settings, from 4x4 to 10x10)
Hover-Car: 7x6, 9x6 (mk1 and mk2 respectively, requires blue science and more)
Crawler: 9x6 (big bulky support vehicle)

Fully Compatible Aircraft Vehicle Mods:

Aircraft (space age update): [8x4, 8x4, 13x12] (gunship, jet, flying fortress; defined internally by mod, not user-configurable.)
9x8 (added to cargo plane, a big bulky support plane)
Lex's Aircraft: [10x4, 10x4, 10x8] (light gunship, cargo ship, heavy gunship; defined internally by mod, not user-configurable)
Helicopter Revival: 8x8 (expensive, more complex aircraft)
Raven: 9x4
Raven mk2: [default 6x6] (user-defined by Raven mk2 mod settings)
King Jo's B-17 Flying Fortress: 9x8

Fully Compatible Watercraft Vehicle Mods:

AAI Vehicles Ironclad: 9x4 (middle-ground between car and tank, in terms of tech)
7x4 (added to ironclad gunboat, when used with the gunboat/mortar add-on)
Cargo Ships: 9x6 (cargo ship, oil tanker, requiring more science than the AAI Ironclad)
9x6 (optionally added to small boat, aquatic boat, boat engine, and cargo ship engine when the Cargo Ships compatibility setting is enabled)

Fully Compatible Train Mods:

Mini Trains: 9x4 (reuses the vanilla train grids, I don't feel they deserve to be nerfed)
Nuclear Locomotives: 9x6
Degraine's Electric Trains: 9x4/9x6 (larger grid with space age, since it's locked behind another planet)
nerfkidjcb's Electric Trains: 9x4 (they inherit the vanilla train grids within their final-fixes)
LuziferSenpai's Electronic Locomotives: 9x6, 12x6 (more expensive than standard trains, requiring batteries, and more complex to run. These values may be overtuned, especially considering the next mod)
SE Space Trains: 9x6 (matching the other electric train mods)
Flamethrower Wagon: 9x6 (militaristic train, matches artillery wagon)
Fusion Train: 9x6, 12x6, 14x6 (t1, t2, t3, respectively; endgame trains, requiring 5 types of science packs)
[OS] Speed Train: 9x6 (requires 4 types of science packs)
Better Train System: 9x6, 9x8, 12x10 (t1, t2, t3, respectively; requiring 3, 4, 5 types of science packs; possibly overtuned?)
5Dim's New Trains: 9x4, 9x6, 11x6, 12x8, 13x10 (t2, t3, t4-t6, t7-t9, t10, respectively; no clue how to balance 5dim's, but this seems fine)
Armored Train (Turret Wagons): 9x6 (added to armored locomotive mk1; combat platform grids keep their original dimensions, but are updated to use cargo vehicle equipment categories)

Fully Compatible Miscellaneous Mods:

Napu's Mod: 9x6, 11x6, 12x8, 13x10 (t2-t5 cargo wagons; no clue about balance for this mod)
Laser Tanks: [10x5, 10x10, 10x10] (electric car, electric tank, electric locomotive; defined internally by mod, not user-configurable)
Also adds electric vehicle related equipment, which remains exclusive to electric vehicles.
Schall Tank Platoon: [6x5, 8x8, 11x11] (t1, t2, t3 various tanks, user-defined by Schall Tank Platoon mod settings, up to 8x6, 10x8, 12x10)
Schall Armoured Train: [6x5, 8x8, 11x11] (t1, t2, t3 various trains, user-defined by Schall Tank Platoon mod settings, up to 8x6, 10x8, 12x10)
9x6 (added to nuclear locomotive)
Schall Alien Tech: [15x13] (t4 variations of Tanks from Tank Platoon and Trains from Armoured Train when enabled, user-defined by Schall Alien Tech mod settings, up to 16x14)
Schall Gun Pod: Equipment similar to Gun Turrets, but very specifically tailored for the Schall Tank Platoon and Schall Armoured Train mods. These restrictions were not modified, as the equipments do not appear to be intended for all vehicles.
Prometheus Grenade Launcher: Another variation of firearms as equipment, this time using custom grenade launcher and ammo, with a relatively wide minimum firing distance (likely to prevent self-damage from the explosions)
Also adds a new tank, which used the 6x8 power armor grid (modified to the standard tank's 9x6)
SA-Humvee: [8x8] (user-defined by SA-Humvee mod settings, up to 12x12)
SA-T1 Atomic Tank: [8x8] (user-defined by SA-AtomicTank mod settings, up to 12x12)
SA Scorpion: [8x8] (user-defined by SA-Scorpion mod settings, up to 12x12)
Mammoth-MK3: [8x8] (user-defined by Mammoth-MK3 mod settings, up to 12x12)
King Jo's 88mm Pak 43: 7x6 (requires blue and gray science, better than car)
King Jo's Lamborghini Aventador: 7x6 (requires blue science, better than car)
King Jo's Bulldozer: 7x8 (originally shared power armor grid, which is 7x8 after Factorio v2.0.7)
King Jo's Fire Truck: 11x10 (originally shared power armor mk2 grid, which is 11x10)
King Jo's Gigahorse: 7x8 (originally shared power armor grid, which is 7x8 after Factorio v2.0.7)
King Jo's General Purpose Truck: 11x10 (originally shared power armor mk2 grid, which is 11x10)
King Jo's War Rig Truck: 11x10 (originally shared power armor mk2 grid, which is 11x10, applies to truck, train, and wagons)
All other vehicle mods by TheKingJo listed here: Too many to list, but simply changed available equipment categories to exclude exoskeleton legs.

Partial Compatibility With:

Cargo Ships: By default, only the cargo ship and oil tanker are given equipment grids (9x6 to the cargo-wagon and fluid-wagon sections). The small boat can be placed as either a free-roam vehicle, or as an aquatic train, and would not retain its equipment grid when it swaps vehicle types. As well, the engine section of the cargo ship and oil tanker do not retain their equipment grids when mined. However, this can be overridden in the settings, giving each boat a 9x6 grid.
Bob's Vehicle Equipment: This mod already provides equipment grid functionality to all vehicles, and also generates its own vehicle-specific movement bonus equipment. Vehicle Logistics settings still apply.
Krastorio 2/Spaced Out: This mod already provides equipment grid functionality to all vehicles, and also generates its own vehicle-specific movement bonus equipment. Vehicle Logistics settings still apply.

Incompatible with:

NONE: There are currently zero fully incompatible vehicles, as none have been reported (yet).

If you have a vehicle or equipment mod to add to the specific compatibility list, please don't hesitate to post the suggestion as a new thread on the Discussions tab.

Vehicle Equipment Grids