The Viridian Room first.
The Crimson Room is perhaps the most famous (and the smallest) such game however, there is one clue that requires going to a specific URL and last time I tried to play it the information was out of date and did not work. This may have been fixed; you’ll know it when you see it! Lots of other similar escape games at Escape Room.
As always, do try to solve the games by yourself – searching for walk-throughs is a sign of defeat!
Digital escape games have given rise to real-life versions. If you're in Bangkok, have a look at Escape Hunt.