Why would a GFCI trip on refrigerator circuit?
Residential Kitchen

In a dwelling unit (residential), GFCI protection is only required for kitchen receptacles that serve the countertop surfaces. There's no requirement to GFCI protect receptacles that serve a refrigerator. Unless the fridge is plugged into a countertop receptacle.


  National Electrical Code 2014
  
  Chapter 2 Wiring and Protection
  
  Article 210 Branch Circuits
  
  I. General Provisions
  
  210.8 Ground-Fault Circuit-Interrupter Protection for Personnel. Ground-fault circuit-interrupter protection for personnel shall be provided as required in 210.8(A) through (C). The ground-fault circuit-interrupter shall be installed in a readily accessible location.
  
  (A) Dwelling Units. All 125-volt, single-phase, 15- and
  20-ampere receptacles installed in the locations specified in
  210.8(A)(1) through (10) shall have ground-fault circuit interrupter protection for personnel.
  
  (6) Kitchens— where the receptacles are installed to serve the countertop surfaces.


Garages, Unfinished Basement, and Other Locations

If the refrigerator is in a garage, boathouse, or unfinished basement. All the receptacles are required to be GFCI protected, so the fridge will have to be plugged into a GFCI protected receptacle.



Why does the fridge trip the GFCI?

Any inductive load when switched off, can produce electromagnetic interference (EMI). This interference can, and often does, trip GFCI devices. Most vapor compression refrigerators have a few inductive loads, any of which could cause the trip.

Is there anything that can be done?

There are devices called snubbers that can be used to reduce, or eliminate the effects of EMI. Installing one between the fridge and the GFCI device, could prevent nuisance trips. The best solution though, is to connect the fridge to a non-GFCI protected circuit.

If that's all it takes, why isn't there already one built in?

While most (all) manufacturers are aware that refrigerators can cause nuisance tripping of GFCI devices, most (none) seem willing to provide a solution. It would be complete speculation for me to try and tell you why they don't care, so of course I'll go through a few possibilities.


Cost.
Plain and simple, it costs money to implement a solution.  
Warranties and Operating Conditions.
Most refrigerators are designed to operate in a kitchen. Running them in dusty, dirty garages and basements could lead to more warranty covered repairs.