Yes, several classic Halo titles are playable on the Xbox 360 via backward compatibility. Here is the breakdown:
Important Notes: Original Xbox games require an official Xbox 360 Hard Drive to run. While the original versions work, the Anniversary editions offer updated graphics, terminals, and skull modifiers. For the largest library—including Halo 4, Halo 5, and Halo Infinite via cloud—consider Xbox One or Series X|S consoles.