which categories do you have in your steam library?

Wow, Didn't even know you could do this. Time to clean up my library.

• Free
• Indies
• Bad indies
• Finished indies
• Bad Games
• Finished Games
• Valve Games
  and then all the others which is not a category, is just where they go when you activate them

Simply like that:

• Major Bullshit (Bad Rats for example)
• Crap
• Yawn
• OKish
• Good
• Cool
• Awesome
• Heavenly
• Better than Sex
• Better than Beer
• Better than Football
• Drugs (World of Warcraft added as non steam game)

I also have a special category named "I love ponies".
In there, I drop any girlish games I have.

Favorites
~Actually Now Playing~
~Now Playing~
Alpha #
Alpha A
...
Alpha Z
Demo
Early and Test Versions
Emulators
Mac Version
Other
Unowned

"Favorites" is just the "Favorites" Steam default category.
"Actually Now Playing" is recent. It has only 2-3 games in it. "Now Playing" has about 10-15....
The "Alpha(betical) #, A-Z" categories have lasted me maybe two years, give or take. It's better in those categories rather than the default unsorted alphabetical for two reasons: 1) I can sort things like "Lara Croft and the Guardian of Light" and "Final Doom" under T with all the other Tomb Raider games or D with all the other Doom games. And 2) I can tell whenever there's something new in my library that I haven't yet sorted into a category, since it'll be under Steam's default "Games" category at the very bottom of my list.
"Unowned" is usually just where I put expired demos/betas. "Other" has non-games in it. The rest should be self-explanatory.

Favorites
Beta
Completed
Not worth my time
Games

Co-op, Multiplayer, Singleplayer, Mods and the inevitable "Games" category where games I either don't know shit about or don't give a shit about go.

I've smashed my head against the wall for quite a while trying to find a system that works best for me (399 games + a few non-steam). This is what has worked well for me, though my Strategy category is a bit bloated because, if I can't think of another genre for a game and it requires any forward-thinking, I just stick it there.

Action
Adventure
Defense
FPS
Online-Only
Platform
Puzzle
RPG
RTS
Sandbox
Simulation
Strategy
Zzzz (junk category)
[Completed] (100% games)

A Valley Without Wind, Alan Wake, ARMA, Back to The Future, Batman, Bioshock, Borderlands, Commados, Company of Heroes, Dead Space, Deus Ex, DOOM, EdmundM, F.E.A.R., Fallout, Farcry, Garry's Mod, Genre: Action, Genre: Adventure, Genre: Horror, Genre: Indie, Genre: Multiplayer, Genre: Platforming, Genre: Racing, Genre: RPG, Genre: Sandbox, Genre: Strategy, Grand Theft Auto, Hitman, Indie Bundle 2, Indie Bundle 3, Indie Bundle 4, Indie Bundle 5, Indie Bundle 6, Indie Bundle 7, Indie Bundle 8, Indie Bundle Android, Indie Bundle Android 3, Indie Bundle Android 4, Indie Bundle Android 6, Indie Bundle Doublefine Amnesia, Indie Bundle Frozen Synapse, Indie Bundle Introversion, Indie Bundle Origin, Indie Bundle THQ, Indie Bundle Voxatron, Indie Bundle Weekly PDP, Indie BundleinaBox Eclectic, Indie Bundlestars #6, Indie Gala 1, Indie Gala 11, Indie Gala 3, Indie Gala 4, Indie Gala 5, Indie Gala 6, Indie Groupees BAB, Indie Groupees BAB4, Indie Groupees Be Mine Bundle 2, Indie Groupees Be Mine Bundle 3, Indie Groupees Be Mine Bundle 5, Indie Groupees Be Mine Bundle 6, Indie Groupees Be Mine Bundle 8, Indie Groupees Build a Doujin, Indie Groupees Damned Bundle, Indie Royale Fall, Indie Royale Lunar, Indie Royale May, Indie Royale Mighty, Indie Royale Winter, Indie Royale Xmas 2.0, IndieGamestand Geneforge Bundle, Just Cause, Mass Effect, Men of War, Music Games, Oddworld, Penny Arcade's OTR-SPOD Series, Penumbra, Poker Night, Red Faction, Red Orchestra, Resident Evil, Saints Row, Sanctum, Serious Sam, Shadowgrounds, Shoot Many Robots, Sonic the Hedgehog, STALKER, The Elder Scrolls, The Ship, VALVe, Warhammer, X-COM, and Games.

Depressurizer is wonderful for handling your categories list. It's way easier than Steam's built-in functionality and will save you a lot of time.

My categories:

Favorites (games I'm playing now)
Action
Adventure
Casual/Puzzle
Multiplayer (regardless of what genre it is)
Platformer
Racing
RPG
Shooter (FPS and 3rd-person shooters)
Simulation
Strategy
Zee junk (so games I never want to play again are kept at the bottom of my list)

I sort by publishers.

I've been thinking about changing that up, though, and do it by developers instead. That way it won't get messed up when publishers go bankrupt, like happened with THQ.

Favorites
Games

Action(getting long so I might split it up again)

Action RPG

Action Sandbox

Adventure

Extras (where I leave betas and demos)

HDD (for games that I didn't purchase on Steam)

Horror

Online Only

Platformer

Puzzle

RPG

Simulation

Strategy

Strategy RPG

Unplayable (where I put the Mac versions of the GTA games)

I should probably update it to be more specific later on.

My categories are named Junk (uninstalled crap), 1x, 2x and 3x. I sort the games according to their scale (graphics and size of game-world). It's a bit odd, I know, but it makes it easier for me to see which games I want to play. An unsorted category just creates a big mess in my head, and more defined categories would leave me frustrated as there would be too many.

My catagories:

• Completed
• Currently Playing
• Demos
• Media/Other
• Meh (Games I tried, and don't like. Will not complete)
• NON-Steam
• Steamgifts (to prioritize playing SG games)
• Games (Basically "the rest")

Favorites

Backlog

Games

The Backlog category is larger than the other two sections combined :/

Installed, NotInstalled, WillnotPlay, ToInstal, Finished

Nope, don't have any.

• Games made in Botswana
• Games featuring Nicolas Cage
• My Little Pony/Amnesia crossovers
• Badger simulators
• Games that DO NOT have Batman
• Secret of Magic Crystals
• Games whose lead programmers names start with "G"

Mods, Indie, Shooter, RPG, and the other stuff

"bad rats" and "other games"

I use the Grid, but my games are categorized as follows:

Assassin's Creed

Because I'm... (this contains my Batman games)

Bethesda

Co-Op Games

First Person Shooters

Indie Games (mostly bundle games that I never play, but there are some good ones in there like Super Hexagon and Audiosurf)

Open World

Racing Games

Third Person Shooters

Valve Games

Will Never Play

Favorites - Games I am playing or plan on playing soon. I only install the ones I'm actively playing, so the white/black is a good indication of which is which.
Great Stuff - Games I will likely add to favorites, sequels of games in favorites, etc.
Already played - Games I am pretty much done with (maybe a replay years down the road, but done for now). I keep this list hidden.
Replayable - Games I'm not actively playing, but are fun to turn to now and then or might want to replay in a year - Team fortress, binding of isaac, meat boy, bastion, etc.
Tentative No - Games I'm not likely to want to play any time soon - A lot of bundle games end up here, bwaha. I hide the list.
Unplayable - Ick. Tried and didn't like, bundles I have no interest in, etc. Hidden list.
Unsorted (default) - Games I'm not sure about, go through periodically and add to favorites/great stuff if I want to try something.