A lot of games have mods. Some of them even improve things or outright make the games actually playable.

For example, my Go To mod for Starbound is FrackinUniverse; an expansion sized mod which adds loads upon loads of content, helping to fill in that spacious void that Chucklefroth left.

I know a lot of people swear by GMDX for playing Deus Ex, and there are countless mods for Elder Scrolls games.

What mods for which games do you prefer, and why?

For the ES games, the Unofficial patches because those guys fix things Bethesda couldn't/wouldn't.

Generally any mod that fixes things and adds QoL to a game. Used to be Grim Internals was essential for Grim Dawn, but several of the features have been added to the base game.

Jagged Alliance 2 - The 1.13 mod since it gives the game more depth and makes your mercs a whole lot more customizable.

Mount and Blade: Warband - The Diplomacy mod because of the needed graphical tweaks and several quality of life improvements. For instance, you only need to search for a village's elder or a town's quartermaster once, and then afterward you can contact them via a menu when you visit the location.

Doom - The Brutal Doom mod, because it's insane.

Evil Genius - Technically it is a mod, if only a minor one. You alter one of the config files to allow you to have double the amount of minions. The normal limit of, 100 iirc, becomes problematic late game because of the number of different classes - valet, spin doctor, soldier, sniper etc.

Do opensource clones count? In that case, OpenXcom for the original UFO game and the Terror from the Deep expansion. It adds a ton of quality of life improvements, such as proper higher resolutions support and the ability to strafe. In the same vain there is also OpenTTD and OpenRCT2.

I considered such a criteria, but considering they run via a separate executable package and in the case of OpenTTD, is completely freed of the original code, I'm not certain they really count.

My mods for Skyrim and Fallout 3/NV are mostly the top rated community patches so they actually run ok, haha. I spend a lot of time in Skyrim, so I've also accumulated a lot of other mods I pretty much never play without - things like Wet and Cold, Pure Waters, Enhanced Towns and Villages, Vurt Flora Overhaul, Whistle (so I don't keep forgetting where the damn horse is).
Ghost Recon has some really neat mods, ranging from new weapons and uniforms to entire campaigns. Frostbite and Aus_Viper's Australian campaign (forgotten what it's called), are very good.
CMT has done some amazing work for Halo Custom Edition. Honestly, if you have access to Halo CE and don't have any CMT maps ...

The BUG mod (Beyond the Sword Unaltered Gameplay) for Civilization IV. It's an interface mod that rearranges the information that is already available in-game, making it a lot more accesible and clearly visible. You can customize how much information you want displayed. It's so useful that some people believe at first that it's cheating, but it's just making instantly available to you what otherwise would require a handful of clicks.

Age of Empires 1 - uPatch. Adds 99% of what the "HD" / "Definitive" do to the originals without the trashy DRM / rebuying the same game at ever inflated prices over and over and over (and the community patched UI is even better than the official 'enhanced' one...)

Age of Empires 2 - Userpatch. The AoE2 equivalent of AoE1's uPatch.

Bioshock - Bioshock Physics Unlocker. Increases the rate at which physics occur in-game ("ragdoll" body movement less juddery) from 30 to 60.

Don't Starve - Amulet and Backpack slots. It feels more like an annoyance removal than a cheat in not having to drop the backpack to put on armor on every engagement and adds a lot to fluidity of play.

Fallout 3 - A lot of bug fixes needed for the usual Bethesda Games need. I found GNR Enhanced added a lot to the ambience though, the 100x extra songs fit the tone of the originals well and the variety reduced the monotony of hearing the same few songs being played over and over in a long +80hr game.

Morrowind - MGE XE. Adds so much to the game, from widescreen support and fixing AA to much needed view distance increases. Unofficial patches a must. Plus those textures that replace the "squiggle" on signposts with actually readable names.

Neverwinter Nights - Colorized icon sets. Example. There are other sets for feats & classes.

Oblivion - Darnified UI is virtually required for playing Oblivion on a PC with a keyboard and mouse at typical 2ft distances. Without it, the heavily consolized "stock" UI feels like the video game equivalent of writing a professional job application out in Comic Sans size 24 font... Add on unofficial patches + some minor annoyance removals.

Source Ports - Assuming open-source ports are "mods", Doom & Quake are playing better than ever with GZDoom, Quakespasm, etc.

System Shock 1 - "Proper Logs". For some reason, neither the terse nor full logs match the audio. This mod fixes that so what you read is what you hear when audio logs are playing.

Thief 1-2 - TFix / Tafferpatcher. Widescreen, new DX9/10 renderers, HD textures, bug fixes, and not least it opens up so many great community mods (T2X, Death's Cold Embrace, etc).

Widescreen Patches - Too many to list. From Commandos Behind Enemy Lines to Diablo 2 to NOLF 1-2, modders have done so much to add widescreen support to older games that were never originally coded for them. WSGF is probably the best summary resource.

Far too large a scope for a post. There are necessary patches and mods for so many games. One obvious one not listed above is circle of eight mod for temple of elemental evil.
One useful thing is to look at moddb’s yearly top 100, e.g.

https://www.moddb.com/groups/2018-mod-of-the-year-awards/top100

2019 list will be coming in a few days!!!
https://www.moddb.com/news/top-100-mods-of-2019-announced

Fall From Heaven II is so deep and fleshed out, it's basically a game of its own. So if you buy Civ IV, you get an incredible dark fantasy strategy game for free!

I very rarely use mods, I like to experience games the way developers intended. There are some exceptions though, and one of them is Oblivion's "OOO" mod. The level scaling and stuff are SO bad in Oblivion I really feel like that mod is required, or one like it. I also mod Morrowind to extend the draw distance.

My must-have for Baldurs Gate (Enhanced Edition) is Sword Coast Stratagems, which improves the enemy AI and makes the game more difficult as well as the Gibberlings3 TweakPack for customization of game rules and such.

Thief 2X: Shadows of the Metal Age. Not to replace the main Thief 2 campaign, but as far as I'm concerned, T2X might as well be a canon part of the franchise, and any Thief series playthrough I do will include it. And won't include the awful Thi4f, which I do not regard as canon in the slightest.

Doom I & II & FinalDoom: I recommend GZDoom (Source Port) and Smooth Doom for the vanilla experience. Death foretold or D4T is an amazing Doom 2016 in to classic doom mod.

X-COM: UFO Defense: Skip the DOS version, too buggy (even gog's fixed version) get OpenXcom and find Reaver's Faithful Megamod or Final Mod Pack or X-com files. (I have a mod out for UFO, see if you can find it :) ]

X-COM: Terror From the Deep: also skip the Dos version hardcore (still many unfixed bugs) also get OpenXcom, as for mods? The World of Terrifying Silence by Nord is an amazing mod for it, and I also will shill my TFTD Rebalance mod for it as well.

What specifically does it do?