Here is a list of mods that are currently compatible with K1R.  If you know a mod is compatible with K1R then tell me and I will add it to the list. 
  
These are the ones confirmed to be compatible thus far.  If I have missed any please let me know and I shall add it to the list.  Thanks. 
  
Edit by Fair Strides: 
In an effort to arrange for a decent layout without being able to reserve posts immediately after this post (since we didn't get on the ball when ZM made the thread), I'm implementing some formatting here... 
  
Thus, everything past this point is my (Fair Strides) fault, so blame me...  
  
Compatible Mods (with categories): 
  
Content: 
Bastila on Korriban - K1R Version 1.0 by Fair Strides 
Party on the Leviathan! 1.0 by Fair Strides 
Vulkar Coward Redux 1.0 by Fair Strides 
Malak's Unique Apprentices 1.0 by Kexikus 
Duel Room Final 1.0 by aneeryrlue 
Rece's Upgradable Vanilla Robes by Rece 
Rece's Elemental Robes by Rece 
Rece's K1 Lightsaber Mod by Rece 
Ajunta Pall's Swords Revamped by Rece 
KotOR 1 10 New Robes by Rece 
Canon Galaxy Map for KotOR 1 by Kexikus 
Sandpeople Disguise Drop Fix by Kexikus 
Proper Manaan Quest Endings by Kexikus 
Sithspecter's Boba Fett 1.0 by Sithspecter 
Energy shield Damage Fix 1.0 by R2-X2 
Force Dustil 1.0 by forgetcanon 
Mandalorian Battle Blades 2.0 by Darth InSidious 
Cipher Gear 1.0 by darkbirdie 
Movie Robe Reskin 2.1 by Squall Lionhart 
Saul Karath Enhancement 1.0 by TheImpAdmiral 
Bearded PMHC01 Head Replacement 1.0 by inyriforge 
N7 Valiant 1.0 by inyriforge 
Health Regeneration by MVacc224 
Classes, Feats, Powers, and Skills Tweak by MVacc224 
War Torn Mullet Man 2.0 by ZimmMaster 
Teta's Royal Band Restored by Darth InSidious 
Revan's Jedi Robes 2.0 by ZimmMaster 
Halo Energy Sword 1.0 by Darth InSidious 
Lightsaber and Force Forms 1.0 by Darth InSidious 
Remove Force Power Restrictions on Armor by MrPhil 
  
Texture: 
KotOR 1 Clothing Texture Enhancement by Rece 
Yuthura Sith Eyes with Lightside Transition by Kexikus 
High Quality Starfields and Nebulas by Kexikus 
Green Pazaak Base Cards for K1 by Kexikus 
Darth Malak - Herald of Darkness 1.1 by Kainzorus Prime 
Endar Spire Complete Overhaul 1.0 by  Jorak Uln 
Natural PFHA04 Reskin 1.0 by honeybeenectarine 
Saber Colors Overhaul animated - SWTOR Edition 1.0 by Jorak Uln 
No Dark Side Transitions 1.0 by R2-X2 
Advanced Wardroid 1.0 by Xedii/Xarwars 
Malak - Path of Corruption 1.0 by Kainzorus Prime 
  
Incompatible Mods (with reasons): 
Bendak Bounty and Emblem Armor Compatibility Patch by Klexikus 
  - This is merely a patch between two mods, neither of which is currently confirmed to be compatible with K1R, so I'm erring on the side of safety. 
  
Sonic Screwdriver 1.0 by Darth InSidious 
  - Modifies dan13_crattis.dlg, AKA Crattis Yukal's dialog. 
  
Quanon's Saberhilt Pack by Quanon 
  - Confirmed to conflict with Jolee in the Upper Shadowlands. The mod replaces his dlg file, which both undoes the effects of K1R and screws up how it operates in the module. (Thanks to scoutception for finding this the hard way... ) 
  
Questionable Mods (with reasons): 
Scoundrel Trousers by darkbirdie 
  - Because it undoes the fix to the back seam that K1R's Scoundrel texture fixes in the female version. 
  
KOTOR Bug Fix Attempt 1.0 by danii-ch 
  - Some things K1R already does, like Calo's soundset and I believe the Bastila Romance Fix, but I'm not sure how the rest is implemented...