Max Payne 1 & 2 on Xbox Originals
One of the lesser noticed features on Xbox Live is something called "Xbox Originals". This is a feature where complete Xbox 1 games can be downloaded from the Marketplace, and you can play them on your Xbox 360. If you'd like to read more about the details of the originals program, you can do so here. Microsoft used to give this away for free for awhile via "Backwards Compatibility", and that still does work, but they stopped working on free updates to that right about the time that Originals came out on the 360.
Anyway, available now on Xbox Originals are the first two Max Payne games. These games were both released some years ago when the Xbox 1 was the current console from Microsoft. They've been out of print on physical media for some time now. You can occasionally find them for sale cheap still when a store decides to clear out old inventory. But starting now, you can get them any time you want digitally for 1200 Microsoft Points each.
If you click on the two box art images below, you will be taken to each game's respective page on the Xbox LIVE Marketplace. From there you can use another little known, but very cool feature where you can buy the game online, and then the next time you turn on your 360, it will start downloading immediately. That works for anything in the Marketplace online. Check 'em out: