House Mods

N'Dib TreeHouse - Eric Henry
Incompatible with TR Map 1+, Third-Party update available
Adds a small island around 30,10. This creates cell incompatibilities with TR_Mainland.
An update was created by abot and is available here: N'Dib TreeHouse Cleaned & Moved [Google Drive]

Castle Draco - Cuchulain
Conflicts with TR, No update available
Adds an island with a castle around 6,-15. This creates (underwater) cell border conflicts with TR_Mainland.
No update is available, but the conflicts do not impede using both mods together.

Wolfen Castle - The Wolfen
Incompatible with TR, No update available
Adds an island with a castle around 1, -16. This creates cell incompatibilities with TR_Mainland.
No update or patch is available at this time.

TODO: Lots more abot patches here

Landmass Mods

Legend of Chemua - Greatness7, MementoMoritius, Melchior Dahrk, TheDrunkenMudcrab
Incompatible with TR Sacred Lands 1+, Third-Party update available
Adds an island with a questline centered around the Nord warlord Chemua. Its placement around 19, -13 conflicts with TR_Mainland.
An update was created by abot and is available here: Legend of Chemua Moved [Morrowind is Home]

The Clockwork Tower - Tsar of Cows
Incompatible with TR, No update available
Adds a landmass around -2, -13. This creates cell incompatibilities with TR_Preview.
No update or patch is available at this time.

Clothing and Armor Mods

Better Robes (TR Addon) -  Moranar
Incompatible with TR1512+, Third-Party update available
Replaces vanilla robes with NioLiv's robe meshes. The TR Addon has been broken since an internal file path change in December 2015.
An update was created by Atrayonis and is available here: Better Robes - Updated Tamriel Rebuilt Patch [Nexus Mods]

Creature Mods

Morrowind Comes Alive v8.2 (TR Addon) - Neoptolemus
Incompatible with TR1609+, No update available
Adds NPC spawn points to exteriors of Vvardenfell and (via addon) to the Mainland. The IDs for clothes, armor, and cells are all pre-Tamriel_Data and release 16.09. Applying the filepatcher will correct some problems, but not all.
Unfortunately, the restrictive permissions of MCA do not allow for an updated TR Addon to be released by a third party. A cleanroom reimplementation has yet to happen.

The Undead (TR Addon) - Neoptolemus
Incompatible with TR1609+, Filepatcher works
Adds additional creatures to undead levelled lists of the Mainland. The levelled list IDs are all pre-Tamriel_Data and release 16.09.
Applying the filepatcher will solve the problems with the addon.
Unfortunately, the restrictive permissions of The Undead do not allow for an updated TR Addon to be released by a third party. A cleanroom reimplementation has yet to happen.

Overhauls

Morrowind Graphics and Sounds Overhaul (MGSO) - kingpix
Conflicts with Tamriel Rebuilt, Do not use
The Morrowind Graphics and Sounds Overhaul was an early attempt to create an easy-to-use modpack. It suffers from various ailments, such as being essentially outdated (many mods it contains have been updated since, including critical updates to the elder scrolls Mod Load Order eXpert (mlox), the Morrowind Code Patch (MCP) and the fork of Morrowind Graphics Extender, MGE XE) and various annoying to game-breaking bugs (from missing Indoril table meshes to containers with essential items no longer containing them).
MGSO's conflicts with Tamriel Rebuilt are mainly centered around the On The Rocks mod (see below) and MGSO's version of mlox, whose outdated database tries to sort the Tamriel Rebuilt plugins accodring to the nonexistant TR_Data.esm (which was replaced by Tamriel_Data.esm in 2016).
Nevertheless, even if the conflicts with Tamriel Rebuilt could be resolved by patching or unchecking the On the Rocks option, we highly recommend skipping MGSO. For a list of reasons, check this thread [Reddit] and this announcement by kingpix that he as author thinks MGSO should no longer be used [Reddit].

Morrowind Rebirth - Trancemaster
Conflicts with Tamriel Rebuilt, Third-Party patch available for older versions
Morrowind Rebirth is in essence a total conversion of Vvardenfell, reimagining it to Trancemaster's ideals with a different balance, landscape, mechanics, and history. Naturally, this conflict with Tamriel Rebuilt's mission to expand the vanilla game as we think the Bethesda developers would have intended it.
The two mods conflict in landscape edits (causing underwater landscape seams), balancing, game mechanics (such as the Guild Guides' teleporting pads), edits to travel destinations, and models (causing floaters and blocking paths in mainland Morrowind).
While Trancemaster warns against using both Morrowind Rebirth and Tamriel Rebuilt together, they merely conflict but are not actually incompatible and can be used together with a bit of deliberate cognitive dissonance.
A patch created by Dreamer fixes the incompatibilites and removes/revamps Morrowind Rebirth's balancing (Morrowind Rebirth - Tamriel Rebuilt and Gameplay Patch [Nexus Mods]) up to version 5.1.1 and 20.02 respectively.

Miscellaneous

BTB's Game Improvements - BTB
Incompatible with TR1807+, Third-Party reimplementation available
Changes various game settings in order to create a different balance and fix shortcomings of the base game.
Unfortunately, the "Settings" part of the mod switches every single exterior cell to "Illegal To Sleep Here", thereby overriding cell names and region placements of TR. This made both mods incompatible when Old Ebonheart moved from TR_Preview (overriding BTB's ESPs) to TR_Mainland (being overridden by BTB's ESPs) with release 18.07. The cell name incompatibility creates dialogue and script errors, most notably TR_m3_oe_act_haybale_script, which tends to crash the game on startup.
Forks of BTB's Game Improvements, lacking the changes to the exterior cells, were created by Sigourn (BTB's Game Improvement - Sigourn Fork [Nexus Mods]) and Necrolesian (BTB's Game Improvement Tweaks [Nexus Mods]).

Tamriel Rebuilt Improved Inns (or NOM) Add-on - Skrawafunda
Incompatible with TR1508+, Third-Party reimplementation available
Extends Taddeus' Improved Inns [MW Modhistory] functionality (which was later merged into Necessities of Morrowind [MW Modhistory] of being able to choose wether an inn room should be rented for 1, 5, 15, or 30 days to the Mainland.
Unfortunately, the mod was never updated after the Sacred East release (missing newer inns) and also sets scripted ownership flags to containers for the duration of the rented period, which would require an update on every new TR release.
A recreation of Improved Inns, including an up-to-date TR patch, was created by RandomPal and is available here: Improved Inns Expanded [Nexus Mods]

On the Rocks! - Taddeus
Conflicts with Tamriel Rebuilt, No update or patch available
Replaces rock meshes with differently shaped, more detailed ones. While the original mod includes bump maps and such, "lite" versions exist that merely replace the models.
However, all of these change the rock shapes, which leads to TR exteriors relying on the vanilla shape to block off certain paths or doors or create holes in the landscape.
No update or patch is available. For compatibility with TR, mods that do not change the shape of rocks are suggested.