which categories do you have in your steam library?

Not Installed

Completed (100% Achievements)

Also have a Movies for Indie Game : The Movie and incase anything else like that get's added to steam.
Then I just have my installed games as 'Games'

I group games of the same series / franchise together.

(Batman, Sonic, Serious Sam, Tomb Raider, etc)

100% / Backlog / Complete / Crap / Current / Indie / Mac / MMORPG / Multiplayer / New / Nostalgia / Prerelease

none

Just aphabetical order.

Complete
Need Computer
Will Never Play
Prototypes
Games

Default; alphabetical + a few Fav's.
Recently that Halflife thing I have from Deathmatch or so has started it's own category, "other Games". oO

Favorites - installed
Games - not installed

I tried having an alphabetical system, but it became extremely tedious to find things without using the search function. So now I have a huge favourites section for frequently played games and a couple extra categories for 100% achievement hunting and card drops. Nice and basic.

-100% finished
-Finished
-Multiplayer
-Sandbox
-The rest

Action
Adventure
Beta
Casual
FPS
MOBA
Movie
Multiplayer FPS
Non Steam Games
Platformer
Puzzle
Racing
RPG
Strategy
Tip Down Shooter
Tower Defense

Also, I use the Installed view as default.
It's the best I could think of but unfortunately it's kinda starting to fall as I get more games.
I would love to be able to create sub categories, at least by series, if not more complex subcats and the posibility to add a game to multiple categories.

Favorites and the rest.

I gave up on making categories as soon as I found out they're not saved to cloud.

backlog (always closed)
Racing
Flying
Indie
Have to play that
different (steam games of my 2nd account, so that I do not always see them)
Games (for AAA stuffs)

All the games in my library are set by game series.

Favorites - Used for games that I'm currently playing/recently played. Mainly trading card games and games I've been playing with friends.
Demos - Just Steam demos.
Fake Games - A notepad (or another .exe file) simply renamed after a fake game, example: "Mass Effect 3: Better Ending Edition", "Half-Life 3", "[Any game with an online mode] Beta". Also a notepad file renamed after a game I'm playing on a console, example: "Saints Row IV - Xbox 360"
Non-Steam games - Installed games that aren't on Steam.
Games - Games I don't feel like putting in a category at the moment.

To add to my reply above, I've just found an application called Depressurizer.

It apparently has an option to auto categorise games according to their genres.

I'll try it out tomorrow when I get back on my computer.

i dont do cats, its for the birds

Two. One for the games I'm currently playing / multiplayer games / demos. One for games I have finished.

Installed games, and good to go

favourites / trash / games i havent played or dont like

100%
Completed
Not Playing
Everything else

100% - Games with all achievements unlocked (or finished if they don't have any)
Betas - TF2 beta, L4D beta and others I don't want to be bothered with
Never to be played again - Games I tried and uninstalled right after
To be finished someday - Games I haven't completed or 100%'ed but I am goig to sometime in the future
Games - Everything else that I haven't decided what to do with or doesn't fit to any category.

• Playing
• Backlog
• Completed - not necessarily 100%, just finished the main story
• Retired - mainly multiplayer games that can't really be completed and I've had my time with them; hence, they're "retired", so to speak, e.g. Age of Empires III, Killing Floor, Bad Company 2, L4D, TF2. I've always thought that it's a bit of an iffy category, so if someone has a better name for it, I'm happy to hear it.

The rest of my games are dumped in "Not Installed"; they're basically games that I gave up on or never plan on playing, and I pretend don't exist!

Local. Secondary (external). Online (for those requiring steam connection, subcategory of Secondary). Extraterrestrial.

• Current
• Favorites
• Priority (Priority, Backlog, and Backlog 2 are all pending games to try)
• Unfinished (Games I haven't finished but am interested in finishing at a later date)
• Unfinished 2 (Games I thought were ok but didn't finish)
• Unfinished Pending (Games with more content pending or difficulty events/achievements I still want to unlock)
  Backlog
  Backlog 2
  Chicken (scary games for whenever I feel ballsy)
  Continue (MP games that I have enjoyed)
  Finished
  Garbage (Bad Rats, Crazy Machines, Shadow Harvest, Ravaged, Blacklight: Tango Down, you get the picture)
  Indifferent (Unsatisfactory time spent, zero interests in continuing; different classification in case I want to give it a second chance)
  Miscellaneous (Betas, Prototypes, Unused Duplicates
  Tried & Done (Satisfactory time spent exploring the game, zero interests in continuing)
  Unsorted Bundle Games
  Unsorted Collections (GTAs, Tomb Raiders, Men of Wars, Serious Sams, etc)
  Games (haven't sorted at all)
  And I still don't think I have enough categories.
  Edit: The bullet points are actually hyphens so that they appear earlier in the category list