ADX

ADX is a sound format used in Bayonetta. It was developed by CRI Middleware and first used in 1996 for Sega Saturn titles.

AtomENCD
AtomENCD is a GUI interface for adxencd by DuIslingr that provides all the same features, but with a user friendly appearance. Note that you must include adxencd.exe to use this program.

adxencd.exe
Commandline tool ADX Audio Decompression Tool v4.61 can be used to encode or decode ADX files. Using samples, you can even set loop points for a BGM track. Download adxencd.exe here.

PES Sound File Converter
PES v1.8 can also batch convert WAV files to ADX and back. You can download PES here.

XMPlay
XMPlay is a third party music player with a simple UI which allows high quality .ADX playback and encoding. You are able to encode .ADX files into FLAC, MP3, OGG, and more. However, converting to .ADX is not possible using XMPlay. Download vanilla (No plugins) XMPlay here, or download the all-in one folder (Contains plugins which allow .ADX playback and encoding) here.

VLC Media Player
VLC media player can play ADX files.

VGMGUI
VGMGUI is a graphic interface of VGMStream which already has loads of plug ins (foobar2000, Winamp, etc) but VGMGUI is made especially for VGMStream. This program allows you to get metadata from files, specify loop count, fade time, fade delay, play files, mange list of files, search files, and convert files to wav. The forum post is here with a download