343 Industries has announced that it will be shutting down online services for the Xbox 360 versions of its Halo titles next year, in order to focus resources on Halo: The Master Chief Collection and next year's Halo Infinite.
The games effected include Halo: Reach, Halo 4, Halo 3, Halo 3: ODST, Halo: Combat Evolved Anniversary, Halo: Spartan Assault and Halo Wars and will all have their online services shut down by approximately December 2021. Though all seven titles will remain playable indefinitely online features such as online matchmaking will be limited or disabled.
It's important to note two cavaeats with this news: yes, it does effect the backwards compatible versions of these games if you're playing them on Xbox One or Xbox Series X|S, but it does not effect the Halo: The Master Chief Collection versions of each game, as 343 say they have been rebuilt and remastered to use entirely modernised services. The move also does not effect Halo Wars: Definitive Edition on Xbox One and PC.
As of this weekend's announcement, all seven games are no longer available to buy on the Xbox Store, and you can check out a graphic that explains which parts of each game specifically will be effected below. You can also check out the full explanation from 343 Industries themselves over here.
The next 343 Industries Halo title—Halo Infinite— is currently aiming for a 'Fall 2021' release on Xbox Series X|S and PC after having missed its originally intended launch alongside the Xbox Series S and Xbox Series X consoles.