I went through the mods at MATY to find Critical and Very Critical mods. Here's my list, based on Pescado's hack rating system:

Woohoo LTW Fix - http://www.moreawesomethanyou.com/s...pic,6698.0.html
No Unlinkage On Urnstone Delete - http://www.moreawesomethanyou.com/s...pic,2083.0.html (not labeled as critical, but it prevents character corruption, so it looks pretty critical to me.)
No Corrupted Death Memory *CRITICAL* - http://www.moreawesomethanyou.com/s...pic,2368.0.html
Drama Professor & Met Self Fix - http://www.moreawesomethanyou.com/s...pic,4616.0.html
Hygiene Bug Fix *NL ONLY* - http://www.moreawesomethanyou.com/s...pic,1535.0.html
ZOMGPets Job Fixes: Because Maxis Screwed The Pooch Again - http://www.moreawesomethanyou.com/s...pic,5957.0.html
Unofficial AL Patch - Assorted Fixes - http://www.moreawesomethanyou.com/s...ic,12892.0.html

MATY no-regen mods:

NoTownieRegen - http://www.moreawesomethanyou.com/s.../topic,7.0.html
Anti-Redundancy *CRITICAL FOR BVp0* - http://www.moreawesomethanyou.com/s...pic,9607.0.html (this is the no-regen for service sims)
NoDormieRegen - http://www.moreawesomethanyou.com/s.../topic,8.0.html (only available as a part of the director's cut)
No Secret Society Respawning - http://www.moreawesomethanyou.com/s...opic,132.0.html
No Stray Respawns - http://www.moreawesomethanyou.com/s...pic,6027.0.html

Here are a couple of other mods which reduce the number of NPCs:
"Calling in sick no longer generates a useless NPC to clog your data files.":
http://www.moreawesomethanyou.com/s...pic,1479.0.html

Only one professor for each major:
http://drupal.cyjon.net/node/291

Use regular townies for apartments:
http://drupal.cyjon.net/node/220