I just beat A Dark Room. The minimalism was so enthralling. I visualized a world so detailed. I have a very active imagination, so I think I enjoyed it more than even a decently well designed game. It was like reading a novel. Any other games out there like that? Possibly longer? It had a very post-apocalyptic, dark towers, fallout kind of vibe.
Town of Salem is pretty fun! It's free to play on your browser, but there's also a Steam version for $5 I think. I don't think there are any advantages to buying it lol. It's fun to get to know all the characters and figure out how to play them well. Agar.io is addictive too. You really just float around trying to collect the balls, the more balls you collect the larger you become. The circles around you that are bigger than you can eat you. Edit: Added Agar
Tagpro is an awesome, easy to learn, hard to master, multiplayer capture-the-flag game. Love it.
Not sure if this is what you're looking for but you can play Dungeon Crawl Stone Soup online. It's a traditional roguelike with a ton of content that's been getting updates for a decade (and is based on Crawl which was in development for a long time as well).
My favorite is Happy Wheels. It's incredibly absurd and over the top, gory, violent, side scrolling, physics based fun. The levels that aren't user generated are fun but the real fun comes from going user generated and then sort by highest rated. There's an awesome game called... One Chance? I think? It's pretty great but you can literally only play it once. Once you beat it you can't go back and try for a different ending. you can but I think you have to clear your cache and cookies. I haven't actually tried.
If you liked A Dark Room, you might also like Candy Box!
Well, I guess it doesn't really fit your in-post text, but Runescape is my favorite browser game. If you are searching for more browser games though, I highly suggest www.Kongregate.com Probably the best source of browser games on the web.