Well, you can think of using the Due for anything where the Uno does not have enough program space, data space, or pins. You could have used an 8-bit Arduino MEGA instead, but the MEGA is more expensive than the Due...
Here's a little table:
Cost IOS Flash Ram Speed
Uno $30 19 32k 2k 16MHz
MEGA $60 70 256k 8k 16MHz
Due $50 70 512k 96k 84Mhz
The Due may also have a full-sized 64/80bit floating point type, which could be handy for some people.
And a real D-A converter.
Since it's CHEAPER than the closest equiv 8-bit system, the real question is "are there any applications that are unsuitable for a 32bit arduino?" (one that pops up pretty quick is "things requiring 5V IO.)