I grew up playing lots of Flash games, I was definitely a part of its peak moments. In school, it was always a treat to go to the computer lab and be able to get on Miniclip and play tons of different stuff. Later in school, they blocked those types of Flash game websites and instead only allowed you to go on "educational" Flash sites like CoolMathGames. Even on that website there were some awesome games.
Stick RPG is perhaps my favorite I played back in the day. It was a life simulation/RPG game with an overhead view. You played as a stickman and had to work your way to the top by getting better jobs, finding new ways to make money, and upgrading your stats. The goal really was to just reach the end of the upgrade chain.
AdventureQuest is already mentioned here and for good reason, it was very unique to me when I first played it as a kid. Perhaps my first turn-based game.
I was also a massive fan of Interactive Buddy. Having a ragdoll you can throw around and stab as much as you want. IIRC, you earned money by hurting it, and used to money to buy larger weapons to hurt it some more lol.
Run 3 on CoolMathGames was a huge hit in high school. A pseudo-3D runner game where you must dodge obstacles and gravitate towards the walls and ceilings, kids would always brag about who had the highest score. It was our version of the 70s/80s arcade experience.
The Bill Cosby Fun Game to me will forever be one of the funniest games I've ever played. Also the Mcdonald's Video Game was pretty funny and was surprisingly in depth for a Flash game.
I was also a massive fan of Flash animations. Newgrounds is an absolute historical artifact of our time that must be preserved forever. The Xiao Xiao series is one of the first to come to my mind, basically epic stickman kung-fu fights with lots of slow-mo.