Before I recommend any flash games, I wish to promote Flashpoint Archive, formerly called "Bluemaxima's Flashpoint". It is a preservation project not just for flash games, but for potentially all games and animations that were uploaded to the web prior to the proliferation of Facebook, Twitter, YouTube, and other sites such as Tumblr, etc. It is fairly easy to navigate, its built in search function works pretty well (if a bit particular), and it is in even more active development after being open sourced by its original creator (or at least given to other people to work on it in his stead). The version labeled "Infinity" is best for those who don't have entire hard drives to spare.

As for games, I recommend in no particular order:

• The "Learn to Fly" series (You are a penguin, first 2 games you fly a long distance to leave Antarctica, 3rd game you go to the moon. All 3 games are fun, but the 3rd game is probably the most fun to "break")
• Epic Battle Fantasy 3.3: Bullet Heaven (Bullet Hell spinoff of an RPG series, spinoff series has 3 games, main series has 4 or 5)
• Crush the Castle series (4 games total)
• Rage 3*
• Stick RPG
• Thing Thing Arena 2

*Requires going into the config tab and unlocking 18+ games, but you can specifically toggle the pron games as invisible.