Now when/if you download mods for any games, what are your preferred ones? Cosmetic mods? Something that affects game mechanics? "cheating" mods?

I mostly prefer cosmetic ones (armor, skins, etc) and mods that make things more convenient. Like the backpack arranger in Skyrim.

What about you?

I care most about gameplay mechanics and balance. I've never had the money, so I generally can't run the best cosmetic mods anyway.

I try to get any mods that fix bugs (aka unofficial patches) and high resolution patches... mostly I try to keep my games as vanilla as possible but current to today's standards.

I usually try for a full polish: Unofficial patches, essential rebalancing, improved functionality, HD texture packs, restored content. Takes a bit of research, and if I'm new to a game, I have to rely on recommendations for these. Still, I avoid user-created content like new models, maps, etc. until I've experienced as much out of the original package as I'm likely to.

Exactly, I like having fixes and functions, but would rather enjoy the game as close to the original experience as possible at least first time through. If I really enjoy a game and want to have something new to try or I find something frustrating then I might look for something more.

It varies a bit from game to game, but usually I prefer minor tweaks, utility mods, bug fixes and the like. I like mods that customize the base gameplay to my preferences. Only rarely do I get around to mods that add new content, or total conversions and such.

At times I'll do some graphical mods, but I'm usually too lazy to hunt down the good ones.

Mostly anything but nude mods and companion mods.

It also depends on the game.

Oblvion needs several hundred mods to fix most of the flaws, while Baldur's Gate only needs Tutu or BGT + Widescreen Mod, BG1 NPC Project and Sword Coast Strategems to turn a mediocre game into a masterpiece.

For turn based strategy games I like mods that increase difficulty/improve AI.

For old First Person Shooters I like mods that give hi res graphics and mouselook. It was a joy playing Doom 1, Doom 2 and Heretic with the Doomsday Engine, for example, or System Shock using SYSTEMSHOCK-Portable.

I generally stick with cosmetic (textures, visuals, etc.) and utility (like toolboks for XCOM EU) mods and stay away from those that modify gameplay mechanics.

I like keeping them as they were meant to be, I add bug fixing mods and maybe a high res mod if the game is really old and low res, I don't like adding skins and stuff to screw with how the dudes that made it wanted it to look.

I like ones that alter the gameplay to create a different experience... not cheating mods, but ones that give more challenge or make it play different from the vanilla product. Brutal Doom and Counter Strike come to mind.

Mostly content additions (as in, quests and such), gameplay additions, spells and such, and ones that make things more convenient. Graphic mods and equipment I've never used.

Usually patches, mechanic changes if I feel a need for them, or content additions - When it comes to the last one, I usually only play mods which have nothing to do with the original campaign, the mods for Half-Life would be a good example of that. The only real exception are TES games, which I tend to mod to hell and back - but only then, I only add stuff I got recommended and a very limited amount of that as well. Usually, modded content is far too obvious in TES games, and you can see on the first glance that it doesn't quite belong. Even for TES games, it tends to be mechanical changes all the way.

First of all bug fixes and patches and then mostly cosmetic mods like better textures, weather/spell effects, altering NPC appearances (think Elder Scrolls games), armor textures etc.

Yeah, graphics updates, bug fixes and 'content restoration' - hoping that the cut content really WAS due to time constraints and not quality
Pretty much mandatory for KOTOR2 though, so I hear...

Edit
OH and then 'total conversion' mods that sometimes blur the line between mods and new games that happen to use the same engine like The Stanley Parable, The Nameless Mod for Deus Ex and NVN user content

mostly cosmetic mods, or mods which makes things run smoother and more stable, but I do use some convenience mods now and then. I do not use mods which change gameplay to much.

For example in Skyrim I have the glowing ore mod (to actually be able to see those damn ores...) and the bandoleer one, which makes me able to craft some extra bags to carry more weight (I am an hoarder). The rest are cosmetic mods.