In October, Microsoft announced game gifting for the Xbox One, allowing users to purchase select games, DLC, Xbox Live Gold subscriptions, and Xbox Game Pass subscriptions for friends and family. It was pretty limited though, and Microsoft says that since the feature has been such a "hugh hit", it's expanding it.
The gifting feature has been expanded to include PC games from the Store, and PC games' DLC. Also, gifting on Xbox One has been opened up to all Xbox One games, rather than just the selection that was previously made available.
While the program is being expanded, there are still some limitations; for example, this still doesn't include Xbox and Xbox 360 games that are playable on the Xbox One via the Backward Compatibility program. Also, there are limits if a product is discounted, so you can only buy two of the same discounted product, or 10 discounted products in total, over the course of two weeks. Finally, the recipient of the gift must be in the same region as the gift-giver.
Microsoft did say that it plans to expand the feature even further going forward. Soon, it says that it will announce gifting of paid PC and Xbox apps. Hopefully, we'll also see gifting of Xbox and Xbox 360 games, along with the ability to gift paid subscriptions to third-party services.