Game Compilation Sites

Flashpoint: a huge archive of flash games, since it's gonna die soon. Feel free to contribute in the name of preservation!
Kongregate: one of the cleanest flash/HTML5 sites. I've found some fun stuff here, and the achievement system is well-made.
Newgrounds: not just games, but all kinds of content. The games are the main point, though.
Cool Math Games: an absolute classic. Has a lot of ads, though.
HoodaMath: less ads, but less games. Currently in a transitional phase due to Flash's future death.
Math Is Fun: Third verse, same as the first (and second). Math site with games.
FRVR: a specific company that makes lightweight HTML5 games. They're pretty good.
Interactive Google Doodles: those cool Google logo designs you can actually mess with.
Method of Action: some graphic design games to wet your noodle. Kerning fontypes has never been so fun.
rollApp: meant as a productivity program, it has some simple games that you can play anywhere on anything, because they're not hosted on your computer. You need to sign up for an account, but that's free.
Red Bull Mind Gamers: 6 different games meant to challenge your brain. Don't worry, TFGD isn't sponsored. Requires an account.
Simon Tatham's Puzzles: a random-gen puzzle collection, lightweight and customizable. There's also a mobile app.

jmtb02: the creator of the Exit Path series, Don't Give Up series, and many other elephant games has a website.
OneMoreLevel: basic flash game site with a clean interface. It's pretty cozy.
HTwins.net: the creators of BFDI and The Scale Of The Universe have done a lot.
Memory Improvement Tips: A collection of 270 games, mostly simple stuff. Most can open in a seperate window for a better experience.
Learn4Good: hundreds of games in every category. They say they've been in the game for 12 years!
Hyperspeed Gaming: my friend's site acts as a quick portal to a few things. He also has a link for device repair, but it's probably only for local folks.