Matt,
I've implemented A/Ds up to 18 bit resolution. Above 12 bits, things may become problematic. Generally, four areas *MUST* be taken care of:
1. Trace layout. We generally keep the analog traces on a different layer, sandwiched by two ground planes on the PC board. Proximity and orientation of the A/D closest to the analog signals is really important. Winding A/D traces thru the digital lines is suicide.
2. Power supplies. We NEVER use the digital supply for the A/D, no matter how much bypassing you put on it. We ALWAYS use a separate analog power supply for the A/D and associated circuitry. We ALWAYS use an analog ground separate from the digital ground, that is tied together back at the power supply IN ONE SPOT. Don't forget the analog ground planes already mentioned.
3. We use a precision reference that is placed as close to the A/D as possible, properly bypassed, and using the analog power supply.
4. On some especially sensitive applications, we use an interposing latch that further separates the digital outputs of parallel bus based A/Ds from the uP's data bus.
On a final note, are you using the right type of A/D? How fast are your signals changing? If you can get away with using a dual slope A/D, you may consider it. You may also consider some software routines to average several A/D conversions to smooth out the signal. HTH