Magic: The Gathering

Pauper is a cheap format by design, since it's only commons.

Commander is cheap if you buy precons. Very different style of play compared to other formats though. If you want to play with 4 people, it's a great format.

There are also the pioneer or standard precons that Wizards occasionally puts out. They aren't great for actually playing competively in those formats, since Wizards likes to leave out important cards, but they are fun if you are new.