What audio file formats does Android support? What audio file formats does Android (ICS in particular) support? If this depends on the device, how can I find out?
The Supported Media Formats page of the Android SDK documentation (under the "Core Media Formats" subsection) outlines all of the formats that vanilla Android supports. Audio codecs specifically noted are:


AAC LC/LTP
HE-ACCv1
HE-ACCv2
AMR-NB
AMR-WB
FLAC
MP3
MIDI
Vorbis
PCM/WAVE


As the documentation also notes, manufacturers can provided decoders for additional media formats, meaning that this can potentially vary by device a bit. I'm not aware of any simple way to determine which extra formats are supported by a device aside from simply copying a sample over and attempting to play it with the stock music player.

Similarly, specific apps can potentially provide software decoding for additional codecs. MX Player provides codecs in the Play Store, for example.