I'm quite new to itch.io however, these are some browser-friendly games I found and enjoyed:
Probably my favorite browser game I've played on itch.io yet: https://lee-pic.itch.io/guraquest
A fun puzzle platformer I highly recommend: https://cosmicadventuresquad.itch.io/deepest-sword
A somewhat short, yet good metroidvania: https://paranoidcactus.itch.io/ufo
A interactive detective game: https://cajji.itch.io/pirate-fox-detective
One of the first games I played on itch.io: https://joellikespigs.itch.io/ludum-dare-45-you-start-with-nothing
Simple yet fun platformer: https://nastyoldwizard.itch.io/boba
I might edit this as I find more awesome browser games. Please reply with some of your favorites if you have some.
In the rules it says to say why I'm promoting these games. I'm promoting them because they are quite fun and I'd like to recommend them to people.