In brief: Xbox 360 Halo games have been out for a while, entertaining us for many hours since their launch. However, starting January 13, 343 Industries will disable and reduce the online services of many Halo games, but that won't stop you from playing single-player modes as well as splitscreen, Forge, and LAN.
Halo's support FAQ has been updated to reflect which services will be disabled on the Xbox 360 Halo games. These include Halo: Reach, Halo 4, Halo 3: ODST, Halo 3, Spartan Assault, Halo: Combat Evolved Anniversary, and Halo Wars.
After January 13, services like matchmaking, fileshare, MOTD (match of the day), challenges, and extras won't be available anymore. For Halo 4 and Halo Reach, service record and player customization will also stop working, but these services will still be available on Halo 3 and ODST.
Achievements in Halo 3, Halo 4, and Halo: Reach will also be impacted, but not all. Only those that require matchmaking, are based on challenges, or are linked to specific activities will stop working.
You should know that the backward compatible versions of these games for Xbox One and Xbox Series X|S will also stop working. Halo: The Master Chief Collection and Halo Wars Definitive Edition will not suffer the same fate. The titles featured in the collection and the DE use different online services, meaning you can still play them as you've done until now.
While some might not be happy to read this news, we need to consider that some of these games have been available for 15 years. Since then, we've got Halo 5 Guardians, Halo Wars 2, improved versions of most Xbox 360 Halo games, and Halo Infinite, so halting support of some online features is not totally uncalled for.