NXP makes a number of audio DSPs with a native 24 bit width.
Microchip still ships chips in the PIC family with instructions of various widths including 12 and 14 bit however I believe the data memory on those chips is either 8 or 16 bit. I have no idea how to classify a machine where the instruction and data memory widths don't match.
Unlike POSIX, C merely requires that char be at least 8 bits wide. Although I assume lots of real world code would break if challenged on that particular detail.