Is it against NEC code to re-use pulled cable?
No, nothing is wrong with re-using cable and cable assemblies that are listed and approved provided that they are in working order and still permissible for new construction in the location that you intend to use them. Don't use a cable that doesn't have a grounding conductor would be the main rule for re-using what you'd find in a residential setting.

Re-use becomes more of an issue when you get into classified locations, such as medical facilities and other commercial areas. You wouldn't be able to re-use a bunch of MC (metal clad) cable where HCFC (hospital care facility cable) is now required - but you're not likely to run into those situations in a residential setting.

If it's the right type of cable, just test it:


Are the conductors stiff and brittle?
Is any bonding that used to be in the assembly still there, and in good shape?
Is the exterior obviously stressed, or showing signs of damage from smoke or water?


... don't use it :) Otherwise, you should be fine.

Still, even if it looks / tests fine - consider replacing it if it's over 15 years old. You need not waste it, Romex has oodles of uses out of the wall (it's great for tying up/down all kinds of stuff, for instance).