Specifically, the YouTube app will stop working on devices running versions 1 or 2 of Google TV, as well as older smart TVs and Blu-Ray players. While support for the app will be dropped as of the end of April, Google says that it will begin shutting down older versions starting today, April 20.
The shut down of older YouTube apps is being done to accommodate new API changes and features for newer versions. From Google:
As we upgrade the YouTube Data API to bring more features, we'll begin shutting down the old version on April 20, 2015. This will result in the current YouTube app not working on certain device models from 2012 and older.
If you're still hanging onto a Google TV device, versions 3 and 4 will be able to update to a new version of the app and otherwise remain unaffected. Other devices losing support after April also include older smart TVs, Blu-Ray players, and Apple TVs. As an aside, now might be a good time to start looking into picking up a shiny new Android TV box.