I will sometime hang a mic upside-down with the capsule a little above where I would normally place it in relation to a singer's mouth. This can encourage a singer to tilt their head slightly and helps with singing on pitch and can lessen sibilants. I used to do that when recording my own vocals until I found a method that suits me a bit better.
Also, my default setup for ADR/voiceover is to set the microphone upside down, as Bob described, slightly lower than the VO's head and tilted upwards. That way I get a direct line from the VO's mouth to the capsule when they're looking down and reading from a script on the stand.
I quickly found out that a lot of VO artists have some strict preferences when it comes to recording, though - one guy could only get the "voice" he was after if he talked out of the side of his mouth, so that's where we put the mic.
