Due to recent life drama (including fighting two government agencies at once) I will be effectively unemployed for at least the next six months. There's nothing useful I can do with my time.

So I'm looking for a timesink game for PC. I have very little experience of any PC game outside of LoL. Will look into every suggestion; prepared to try anything.

May I offer you some, Final Fantasy XIV:ARR?

Crusader Kings II is brilliant for this. The game really only ends when you're destroyed or get bored of it (since actually reaching the time limit takes a very, very long time). Consider the Game of Thrones mod.

Minecraft? It's the sort of thing I always want to get into but I just don't have the time.

Hearthstone, it's open beta right now.

You should try a rhythm game called osu!. It's completely free and it's a huge timesink. I even got my girlfriend to play it, and she doesn't usually play games on PC. Mind you, it has TONS of Japanese, and in general asian, music, so there's that. For the most part it's not the usual J-pop stuff though. Instead there's lots of music from the Touhou series, and then there's some more music from it. There's some western music too but not as much. Anyway, I don't have any experience with Touhou games but I think those are free too and should be pretty big timesinks. Also, some osu! gameplay here. I failed embedding. There's background and skins and stuff if you want but I think that video gives a pretty good impression about what it's about. Basically you click circles that appear around the screen, and you do that according to the rhythm.

Another recommendation would be Minecraft, for obvious reasons. I don't think it needs introducing

Had no idea there was a PC version. I've never played an MMO. I'm from Europe; would that stop me playing with anyone on VGC?

Fallout 3/New Vegas + mods. I have sooo many hours in those games.

BioWare's Star Wars MMO is a lot of fun to level up with, trying different characters and being Light or Dark. All the classes have different stories.

The Saint's Row games can soak up the hours, too.

Emulators.