So Cookie Clicker has it's own thread, but what about other idle games? I got bored with Cookie Clicker after a few days, and since then I've gotten hooked on a few other similar games.
Currently the only one I have running is AdVenture Capitalist (on Kongregate). I recently hit 2K of everything; 418 tredecillion angel investors.
At one point I had 3 separate games running though... I played Idle Blacksmith up until I reached the max level of everything (before it starts just adding numbers to the names of the things). That one had some neat strategy of trying to even-out the levels of your different productions.
In terms of games that are somewhat idle, but have a lot more to offer... A Dark Room and Candy Box (and Candy Box 2) are all awesome games.