What is the recommended bitrate for Background Music in iPhone Games?
In all honesty, it's probably down to what sounds best at the lowest bitrate.
So if you had music at 192kbps but you could still get it sounding decent without a whole lot of quality loss at, say, 64kbps, then you've got no reason not to use the 64kbps version.
It might be worth having a bunch of different bitrates of the same song and see which "sounds" the best, whilst reducing the bitrate. If you've got some 8-bit retro sounds in the music you could get away with fairly low bitrates, but probably less so with a piece of music with a wide variety of sounds and textures (e.g. a classical composition, with full percussion, and synths and basses on top).
Just as an extra, if you're not certain about what sounds correct at a low bitrate, I'd suggest talking to an audio producer or if that's not possible then just ask the guys at Audio-Video Production SE those guys definitely know their audio :)
Like Ray Dey said, you need to make the call on quality vs size. Remember the project triangle?
The same applies to audio. You can have good quality audio that doesn't take up a lot of space, but you'll have to manage streaming it and you're often limited to a set number of streaming channels on non-PC hardware. You can have good quality without streaming, but it will take up a lot of memory, etc.
Something to check out, if you are working with composers who would be comfortable writing the music in trackers, you can use FMOD (iPod/Pad/Phone and PSP license is listed under "Casual" on their Sales Page and is $500 flat) and load .MOD, .XM, and .IT. You can have high quality samples and fine-grain control over the flow of music.