Apple Arcade is a game subscription service from Apple. You pay a fixed amount each month and then can play any of the games on Apple Arcade free after that. No upfront payment for each game, no IAP (in app purchase). The games can be downloaded and played without an Internet connection.
Whether Apple Arcade is worth it depends on the individual. I have played a lot of Fantasian, and for that game alone I have found Apple Arcade worth having. But most of the games on Apple Arcade don't interest me.
To primarily help me determine which of the games available are worth my trying I have done a list. There will be errors and omissions in this list, to err is human. But it has been possible to do a list because there are (as yet) only hundreds of games on Apple Arcade.
The list is also an experiment in attempting to meaningfully categorise the games, to organise them by different qualities. These qualities currently are dexterity, difficulty, depth, and genre.
The list can be filtered to omit some of the games.