Note: This app is no longer maintained because it won't work when targeting Android 8.0 due to background service limitations. This app is being rewritten at https://github.com/tobyhs/TimeTalker2.
Time Talker is an Android app that speaks the time.
You'll need to enable this by adding the home screen widget. Make sure your ringer is on. After the screen turns on, shake your phone within a few seconds and your phone will speak the time. You might have to wait a bit as Android's TextToSpeech may take a while to initialize.
The primary use case of this is for me to know the time when I wake up on a weekend and I didn't feel like opening my eyes in case I wanted to go back to sleep if it turned out that I woke up earlier than I wanted to.