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)