On Steam, I organized them by "Completed" "Junk" "Haven't played" and one called "eternal games" where I put games that I'll likely want to play again at some point, usually multiplayer games, sometimes just incredible single player games.
Mainly by console/company. I have one box for Nintendo (Gamecube, N64, Wii, Wii U), one box for PlayStation and PC (PS2 and PS3, only WoW for PC XD) and one box for handhelds (which happens to be only Nintendo, GBC, GBA, DS and 3DS).
Then they're also sorted by franchise, and in order of release (Mario Party 4, then Mario Party 5 for example).
I seem to be the only one to organise games like I do: by title length. You see, all my games are Nintendo ones (I have about 30), and they're Wii U/3DS/Wii/DS, which are all very uniform in terms of titles; i.e. all are centered in the middle of the side, with the same font and colour etc...
So I organise them first by system, and then by title length (So New Super Mario Bros U + Super Luigi U (my longest title) goes on the far left, and Pikmin 4 on the far right, with a nice, clean increasing level of blue background the further right you go, as less space is occupied by the title.
This has the awesome unintended consequence of all my Zelda games being grouped together (by system of course), because the first "row" on the case is always The Legend of Zelda, and the subtitle goes on the second row.
Also, the Nintendo logo is at the bottom of the side of all my games, so that looks nice and consistent as well. All my Wii U games are blue, as in Europe we don't get other coloured ones very often (example; Mario Kart 8 is not red, but blue). The only exception I can think of is Super Mario Maker, but I play that so much it's not ever put on the shelf.
Quite complicated really, but it looks awesome, I must say. I happen to be at the point in time where my total DS/3DS games completely fill a shelf exactly with no space remaining, and my wii/wii U games do the same to another shelf. I'm almost scared of getting Pokemon Moon when it releases, as it'll disturb my coincidental equilibrium! xD
All of mine are organized by system on different shelves. They aren't alphabetical but the different series are grouped together. I really love my 3DS case because it holds almost 30 games and I can have all of them together in one place which is convenient while traveling.
I prefer having a physical copy of a game, than to downloading them, but when I organize them, (which is very rarely, I might add) they go from most loved to least, in series. I dont keep mine all in the same place though. 3DS in one draw, Wii in the other, Xbox in another and so on.
What is this organization you speak of?
Haha seriously though, if there's any sort of order to my games, I suppose it would be that the games I have played recently are at the top of the stack, and those that I haven't touched in a while are near the bottom.
I organize my Wii U games by placing the ones I play more often at the top and the games I've completed or rarely return to near the bottom of the stack. As for my 3DS games, I place them all in the Club Nintendo game cases and arrange them with my favorites on one side and my least favorites on the other side.