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So far I've only made one group: Local Co-OP Games

I don't.

Past year, I've mostly not worried about it and just sorted by "Recent" -- slightly helps with playing games all the way through, although if there was also a "Recent and Installed" sort, that would help a lot. One of the 4K+ Steam Libraries here. I think I stopped trying to sort after around 2.5-3K, where before I did most alphabetical (sorting things like "Lara Croft and the..." and "Something: Total War" both under "T"), some by publisher/developer, and a couple other miscellaneous categories.

I Categorized them by Genre. It took a while but It's the best thing I've ever done.

I used some kind of program to do it by tag, but now I'm stuck with like 6x more games listed because it puts 1 game in several categories. Very annoying, too lazy to fix it.

I use an app called Depressurizer that automatically add user tags to games in steam client, so it is sorted by user tags. I also started to mark games that I want to play ASAP as favorite.

View attached image.

View attached image.

two groups: favorites and non-favorites.
the favorites are the one that I've been playing or the one that is soon-to-be-played.
the trash one is a great idea... I may add this later. :D

By theme, genre, multiplayer and completion.

By bundle ( not too usefull, but the get grouped somehow) : https://i.gyazo.com/a5715da6d2505227f22f3758a2886013.png
By Time To Beat, Release year and Overall score: https://i.gyazo.com/c69a16dd36b2fe66a3bdb455138f7aca.png ( Using Depressurizer, be carefull using it, you can delete your current groups)
Also random groups for freebies or random adquired games: https://i.gyazo.com/97b7ed143ff5208a1779bc9fecf30b39.png
Games that I got in store, got some random categories: https://i.gyazo.com/98cef95963e78f4ee13357732259f5b6.png

Used to organize it with installed and not installed. xD Now, I organize it with finished and not gonna play. xD

I just install any games that I might want to play. Games (583) Installed (28)

"General" for games I would actually play.

"Misc" for shovelware games and free to play games.

have some categories including trash and finished/not finished
I also mark games I'm interested in the moment as favorites

probably need a second trash category, as there are some trash games which I really never intend to play and others I might play one day

In the order that they show:

• Dropped <--definitely won't play again
• Started <--"currently" playing
• Started (without end) <--endless games that are going to remain here forever
• F2P
• Plan to play soon
• Prototypes <--a bunch of double fine prototypes that came in a bundle
• Stuck <--can't finish them for some reason so I gave up but I may give another try someday
• Finished
• Games <--everything else that I have yet to categorize basically

I sort it by the size of the game. My internet connection kinda suck, so whenever im bored with current installed game, i can just quickly pick the best and smallest size to be downloaded.
*I did it manually XD

Beaten:
New Vegas
Dark Souls
Not Beaten
Everything Else

Like that:

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Just 5 categories. All games when obtained go into the "My Games" category by default. I only move them out of there when I have finished with them. If they are games I enjoyed or will play again they go into "Favourites". Acceptable games that are finished (but not good enough for me to favourite) go into "Finished". Other 2 categories are "Rubbish" and "Just For Cards". I only install the games I am currently playing (or card farming). So I usually only have about 20 installed at any one time. Do have this bookmarked (was recommended on one of the steam forum discussions) http://www.lorenzostanco.com/lab/steam/
The library organiser is quite handy and works on your wishlist as well as your library

I categorize them by genre and also have some special sections: "SG wins", "Gifts from friends" - I try to play games from these two first. Then there's "Done" and "100% achievements".

Pardon my french.
But most of them are self explanatory.
I put most of the games in multiple categories.

View attached image.