I used to play flash games a lot as a child. One of my favourites was definitely Line Rider.
I used to play Line Rider all the time as a child. I liked the very simplistic style of the game; so simple, yet so versatile. You had the ability to create your own levels, and even design them with other pens which didn’t affect physics, in which your design could be as complex as you liked. For such a basic idea, I could play the game for hours.
Transformice is another game I obsessed over when I was younger. It’s an online multiplayer game where a group of players (mice) are led by one player (shaman) through different levels. The shaman has powers and there’s a chat system where the mice tell the shaman what they need them to do to help everyone complete the level in the fastest time possible. This game is more complex and has a very distinct design. You can make levels in this too but the entire system is nothing like Line Rider.
Just going by these two games you can see the large variation of games which can be produced on Flash.