There are countless great games you can run ... and 25 classes with the ever-changing landscape of the dungeon. Fallen London is the long-running narrative browser game that preceded Failbetter ...
I remember very clearly being 11-years-old and having to go to a nearby friend's house to play Diablo because the actual gaming PC I had access to at home wasn't powerful enough to run the game.
What are the best browser games? Modern computers are so powerful ... including your mobile phone. If you ever find yourself at an event with nothing to do, send a link to your mates to start ...