I would highly recommend anyone that still likes to play flash games to download flashpoint. Makes it possible to play the games again, and easy to find old classics. And all of them are free.
Some of my personal favorites:
The Phantom Mansion series (puzzle games)
Sonny and Sonny 2 (turn-based RPGs)
Super Mario 63 (a 2D mario fangame based on Super Mario 64, with elements from Super Mario Galaxy and Sunshine as well)
Warframe. I just started this game and it seems really awesome. My only concern is you need Platinum in order to unlock Weapon Slots which means I will definitely have to farm for things to trade with others in order to be able to move up in total Rank and buy Frame Slots. It also seems a lot to take in but I will get there