The nameplate on most fridges is not more than 7.2A. That is the sum of the defrost elements, and all interior lights. Compressors do not run at the same time as defrost elements.
Most residential built-ins, even the huge ones, are not much greater of a load (and how often do you have fridge and freezer open at the same time anyway?
If the nameplate is 10A or more, that's 50% of circuit ampacity, therefore, an individual branch circuit is required. (210.23(A)(2), 2002 NEC, although that only applies to equipment fastened in place, which this appears to be). I don't recall ever seeing this on a domestic fridge, but they may be out there.
It is always the better practice to give the fridge its own circuit. In my area, it's local code as well.