Magic

Magic in a browser game is usually a theme rather than a system, and that's fine - it gives a familiar puzzle a reason to look interesting.

Cut the Rope: Magic is the best of them, taking a physics puzzle you probably already know and adding transformations that genuinely change how you solve it. Sorting Sorcery is a sorting puzzle with a wizard attached, Magic Story of Solitaire does the same for card games, and Idle Magic Academy Tycoon puts you in charge of the whole school. The spells are mostly window dressing on solid puzzle formats, which is no bad thing when the puzzle underneath was already worth playing.

There are 5 free games under this tag, all playable in the browser with nothing to install, and you won't need to learn a spell system to get anywhere in any of them.

The puzzle end sits with Puzzle games, and Fantasy Games is the tag for the wider enchanted run.