Update: If you've already updated, here's how to restore in iTunes and fix iOS 8.0.1 Touch ID and cell issues. If you haven't, Apple has pulled iOS 8.0.1 — even if it shows as available on your phone, don't do it.
Do not install the recently-released iOS 8.0.1 update, especially if you have an iPhone 6 or iPhone 6 Plus. The update brings with it several bug fixes, including fixes to HealthKit, keyboards, and extensions, but it also comes with one show-stopping bug: it kills cellular service and Touch ID on the iPhone 6 and 6 Plus.
We've been able to confirm that iOS 8.0.1 seems to work fine on the iPhone 5s, iPad Mini with Retina Display, and other older iOS devices. As best as we can tell, the issues with disappearing Touch ID support and cellular service are isolated to the iPhone 6 and 6 Plus, which isn't exactly a great showing for Apple.
If you've installed iOS 8.0.1, let us know how it's working for you — and if you happen to know of a fix!