Yes, I read he asked for 16 bits, but I only gave 8 bit examples as its what I saw so far. ;-)
16 bits is still possible, just haven't found an example yet.
Actually, the Arduino Mega, if someone would do a 64k SRAM Shield, it would be possible to use a 16 bit DAC with it via the SPI lines. I'm sure sample rate would be low and sound would be mono, but heck, crazy things could happen. ;-)
I got a 16 bit DAC here that I was testing, and it does work. The problem for you would be the 16 bit INPUT, not the OUTPUT. But still... maybe its time for someone to create a shield that would have a better processor that would handle everything and let the Arduino only control things via the SPI line. Like the GameDuino?
And there's the new Uno32 from ChipKit with the 32 bit processor. It already does audio output, soon someone will do an option for input. Now, if someone would like to donate a Uno32 card to me... ;-) ;-) ;-) http://hackaday.com/2011/06/08/chipkit-sketch-mini-polyphonic-sampling-synth/