Engine

Morrowind Code Patch (MCP) - Hrnchamd
Incompatible with OpenMW
Modifies Morrowind's exe to fix bugs and optimize things. This allows you to scale up the map to show TR's landmass, but still being a fixed size.

Morrowind Graphics Extender XE (MGE XE) - Hrnchamd
Incompatible with OpenMW
Allows Morrowind to render distant views, scenery shadows, high quality shaders, UI scaling and other features. Works with the original engine, so can be combined with the Morrowind Code Patch but will not work with OpenMW.

Morrowind Script Extender Nightly (MWSE) - NullCascade & MWSE Team
Incompatible with OpenMW, requires MGE XE
Makes additional functions available for use in Morrowind scripts, beyond those provided by Morrowind itself. The Nightly version of MWSE also allows event-driven scripting by means of the Lua scripting language. It overrides the stable release that ships with MGE XE and has its own updater script.

OpenMW - OpenMW team
Incompatible with MCP and MGE XE
An open source engine replacer for Morrowind, fixing many bugs with Morrowind's engine. OpenMW allows for better performance of Tamriel Rebuilt on modern hardware. It also allows the map to be as big as your mods need it to be, at a higher resolution than MCP.

Tes3MP - Stanislav Zhukov & David Cernat & OpenMW team
Incompatible with MCP and MGE XE
A branch of OpenMW, it allows for cooperative multiplayer functionality by setting up player-hosted servers. These can range from vanilla-only to highly modded setups. Additionally, Lua-based server-side scripting allows for a very different and new experience,

Bug fixes

Patch for Purists - Half11 & TES3 Community
Patch for Purists supersedes the Morrowind Patch Project/Unofficial Morrowind Patch at this time by still being maintained and limiting itself strictly to bug fixes, with gameplay changes confined to optional plugins. Notably has implemented some bug fixes in coordination with TR and the PT mods.

Expansion Delay - Half11
Fixes overly enthusiastic expansion hooks by delaying the Dark Brotherhood attacks (for Tribunal) and limiting intrustive dialogue topics to a few NPCs (Bloodmoon). Due to its clean and thoughtful implementation, it supersedes most other expansion delayers and anti-nag mods.

Morrowind Optimization Patch - Remiros & Greatness7
This mod greatly improves outdoor (and to a degree indoor) performance in Morrowind, as well as fixing a lot of errors related to flora.

Project Atlas - Melchior Dahrk and the Project Atlas Team
An extension of Morrowind Optimization Patch which makes models use only one texture instead of many, improving performance. Install after Morrowind Optimization Patch.

Landmass Mods

Anthology Solstheim - Atrayonis
Incompatible with most Solstheim mods.
This mod simply moves Solstheim to a lore friendly position, further away from the mainland and Blacklight in particular.

Tomb of the Snow Prince - Wolli and the TOTSP Team
Replaces Anthology Solstheim and is incompatible with most Solstheim mods.
Massively overhauls the hastily-developed Solstheim exteriors in TES3: Bloodmoon, aiming for a quality level consistent with TR and the Project Tamriel mods. The latest version includes Morrowind Optimization Patch's Lake Fjalding fix, Anthology placement, and utilizes Tamriel_Data creatures and items to better integrate the island with the province mods.

Project Tamriel

Skyrim: Home of the Nords - SHotN Team
Adds in a portion of Skyrim into the game: the Reach near Markarth including the two cities of Karthwasten and Dragonstar. Adds 100+ quests including five faction questlines.

Province: Cyrodiil - P:C Team
Adds in the island Stirk located west of Anvil. Currently in beta with minimal quest content.
NB: Not recommended at the moment, as P:C is preparing a full release in the relatively near future that will completely overhaul the island and also add the city of Anvil.

Graphics

Tamriel Rebuilt is built to complement vanilla aesthetics, so we don't recommend much in the way of graphics mods. The default shaders provided by MGE XE or OpenMW already do most of the heavy lifting to improve the game's visuals, without producing any incompatibilities or inconsistencies. That said, there are a few straight improvements over vanilla assets that blend seamlessly into the game, which we recommend:

Familiar Faces - Caleb
Although they have a lot of character, Morrowind's original face meshes were infamous even at launch for their rather sloppy technical quality. This vanilla-purist-friendly mod simply tweaks the face meshes so that they make better use of the original face textures. Instead of the old, oddly pinched and squeezed visages, we get to see what the texture artists likely intended the faces to look like. This mod should be compatible with whichever texture replacer you may be using.

Animation Blending - Greatness7
Requires MWSE or in-development OpenMW
Adds animation blending to Morrowind, enabling smooth transitions between animations. Where before a character would abruptly teleport from one animation pose to the next, now they will seamlessly move between them.
Animation blending for the vanilla engine requires MWSE and the above mod.
Animation blending for OpenMW is included in the base engine starting in version 0.49. Currently you can access it by using in-development OpenMW builds without needing to download the above mod. You will need to turn on the respective option in the OpenMW launcher's settings.

High-resolution Textures

Although the mod is developed primarily with vanilla-resolution (standard definition) textures in mind, we do provide a high-resolution Tamriel_Data version for those who prefer more crisp textures. If you want to use it, we recommend either of the following texture upscales, which bring vanilla textures up to the same size, while holding very true to the original aesthetics.

Intelligent Textures - Remiros
Using AI upscaling, nearly all textures of the original game are updated to a 1024x1024 resolution while remaining crisp. Every texture is carefully curated; textures that upscaled poorly were replaced with hand-crafted versions close to vanilla style.
Contains pre-generated textures for Project Atlas.

Morrowind Enchanced Textures - Project Enhance
Alternative to the above, this is the original AI-based texture upscale mod that covers every in-game texture.
Using this or Intelligent Textures is up to your taste.
Contains pre-generated textures for Project Atlas.

Grass

Tamriel Rebuilt is developed to look good without relying on grass mods (i.e. groundcover meshes), but for those who still like to have dense grass covering the landscape, there is currently one updated option:

Grass for Tamriel Rebuilt v23.1 - Shaord, Rytelier & Remiros
A groundcover plugin to place grass onto the landscape in Tamriel Rebuilt using a blend of Aesthesia Groundcover and Remiros' Groundcover. Now with the optional extra of groundcover in the seas, lakes and rivers.

Miscellaneous Graphics Changes

These are up to the individual's taste.

Near Vanilla Road Sign Replacer -  Atrayonis
A mod for the few people who want to keep graphics as close to vanilla as possible, yet still don't like the illegible road signs that shipped with Morrowind GotY.
Covers Tamriel Rebuilt lands as well as Vvardenfell.
NB: Currently does not cover all Tamriel Rebuilt lands, as it was last updated before the Andaram expansion.

Arukinn-Style Signposts for Tamriel Rebuilt - Red Furry Demon
Requires Arukinn’s Better Banner Signs and Signposts.
This mod replaces all the road signs on the mainland with readable ones similar to those in Arukinn's Better Banners Signs and Signposts. The style isn't exactly the same (would you expect one Mer paint ALL the signs in Morrowind?), but I hope it's close enough. Texture size is 1024x512.
NB: Currently does not cover all Tamriel Rebuilt lands, as it was last updated a long time ago.

Unique Tavern Signs for Tamriel Rebuilt - Rats
A mod that replaces many of the Imperial tavern signs in Tamriel Rebuilt with unique ones for each tavern. Two versions exist, one colored and one with vanilla-style signs. The colored one goes well with Unique Banners and Signs.

Mods aligning vanilla with the wider Tamriel

Beware the Sixth House, Tribunal Rebalance and Bloodmoon Rebalance - Mort
The creatures and NPCs in Morrowind's expansions are extremely tough, as they were initially expected to be played with high-level characters that had already beaten the main game. However, this difficulty often doesn't make sense from a worldbuilding perspective in the context of Vvardenfell and TR. These mods correct the issue by rebalancing the expansions. 

Diverse Khajiit - Taniquetil
All Khajiit on Vvardenfell in vanilla TES III are of the Suthay-Raht subtype. Diverse Khajiit is a simple mod that changes some Khajiit on Vvardenfell to be other subtypes of Khajiit from canon, using the variant Khajiit racesfrom Tamriel_Data. 

Cutting Room Floor - Cicero
This mod aims to be the one stop mod for all cut content in The Elder Scrolls III: Morrowind, and continues to evolve over time, including more content along the way. What this mod is restoring includes items, creatures, quests, NPC's, keys, locations, scripts, spells, sounds, dialogue and voice acting. Cutting Room Floor influences some of the levellists for Tamriel Rebuilt. Cut content Items added by Tamriel Data and Cutting Room Floor share the same stats. The mod will evolve overtime alongside new releases of Tamriel Data and when Almalexia is created in Tamriel Rebuilt.

Quest mods tied to Tamriel Rebuilt or Tamriel Data

Tamriel Rebuilt Introduction Quest - Help a Khajiit reach the City of Good People - Denis418
A short adventure starting near Seyda Neen, designed to give your character a story-based reason to leave Vvardenfell and travel to Old Ebonheart.

Thirteen Telvanni - a Dunmeri Card Game - Dillonn241
Adds a 2-to-4-player, fully playable card game to locations on Vvardenfell, with betting, available at several taverns and other gathering places. Uses the Telvanni suit and Morag Tong card from Tamriel_Data's Dunmer card set. A Tamriel Rebuilt addon is in the works.

Nine-holes - Dillonn241
Adds playable Nine-holes boards from Tamriel_Data to Vvardenfell, with an AI to challenge you and the option to bet gold. Includes an optional Tamriel Rebuilt addon that adds the boards to several locations on the mainland.

Miscellaneous

Better Dialogue Font - Hrnchamd
This mod makes Morrowind's font clearer without changing the font size.

Better Daedric Font - hardek
“A high resolution replacement for the Daedric font used in scrolls.”

Slower Leveling Speed - Varil92
“This mod slows the leveling up of your character in order to avoid becoming overpowered too soon when you have big landmass/quest mods and you want to play all of them with balanced character progression and difficulty.”

TrueType Fonts for OpenMW - akortunov & Isaskar & Georgd
Requires OpenMW
OpenMW is capable of utilizing TrueType fonts instead of Morrowind's font files. This mod consists of a pre-defined setup for three replacement fonts to make users' lives easier.
Use of the optional files Tweaked Texture Buttons and Alternate Pelagiad Font are recommended.

Tamriel Rebuilt Original Soundtrack - Rytelier and ASKII
Requires MWSE or in-development OpenMW
Adds beautiful, original music crafted for TR. Integrates perfectly with vanilla soundtracks and covers all TR areas released up to 2019. Players of the vanilla engine require MUSE2, which allows the tracks to be region, location, and activity-specific.
Players of OpenMW will need the latest in-development OpenMW build (v0.49+) and Dynamic Music.
Those who do not care for the dynamic element can just extract the music files into their Data Files/Music/Explore and Data Files/Music/Battle folders.
NB: Since the mod has not been updated since 2019, not all areas of the mainland are covered any longer.

Preview Warning for Tamriel Rebuilt and How to Create Your Own TR_Preview - Dillonn241
Warns you when you enter and leave the unreleased Preview lands of Tamriel Rebuilt. Also includes instructions how to create your own up-to-date TR_Preview file using the publicly available development files.

Graphic Herbalism - MWSE and OpenMW Edition - Stuporstar & Greatness7
Requires MWSE or OpenMW
Changes the way you pick plants- instead of opening a container, you simply activate them to harvest their contents, with a visual change upon harvest.
As of Tamriel_Data v7, Tamriel Rebuilt flora supports this functionality natively. As such, the use of this mod is highly recommended.

Weapon Sheathing - TES3 Community
Requires MWSE or OpenMW
Shows equipped but sheathed weapons on a character’s hip or back. Includes sheath and quiver models for the vanilla game.Native support for TR weapons is forthcoming; sheath models are currently being added to the next version of Tamriel_Data.

Glow in the Dahrk -  MelchiorDahrk & NullCascade
Requires MWSE or OpenMW
Neat immersion mod to make windows glow at night in settlements with no performance overhead. TR patch included.