Idle, Incremental PC game.
http://www.timeclickers.com/I just found this a couple days ago on Kongregate (
http://www.kongregate.com/games/ProtonStudio/time-clickers) and while I'm still not far into it, I do feel it's the most interesting idle game that I've played recently. The basic idea is that you shoot colorful blocks, get points, spend points upgrading your guns so that you can shoot more blocks faster to get more points faster to upgrade more guns faster and so on...
There are rebirths, dynamic opportunities for rapid advancement, offline progression, and multiple upgrade paths which involve some degree of strategy.
I was initially turned off by the FPS aspect, but once I got used to it I decided it provided some much-needed interaction that has been lacking in other idle games I've tried. If you enjoy idle games but don't care for FPS, I encourage you to give this a shot anyway.
I'm currently at 54 Time Cubes, but I've heard some of the other people in kongregate chat bragging about getting tens of thousands of cubes per rebirth, so I've still got a lot of catching up to do. Right now I'm investing most of my cubes in my Flak Cannon with just enough in Money Multipliers to cover the first tier of each cube color. I'd be very interested to hear if anyone here can come up with a more effective artifact-investment strategy!