Some surge protectors work by "redirecting" surges to the equipment ground, which is pretty much the definition of a ground fault. In this case, it's definitely possible that surge suppressors could be tripping GFCI receptacles/breakers (given a large enough surge).

As for the AFCIs... When electrical contacts separate, they often create an arc between the contacts. This arc spans the gap until the contacts are too far apart, and the arc can no longer be sustained. It's possible (in theory) that the GFCI tripping could create a large enough arc, for long enough to cause the AFCI to trip. It's not likely that a properly functioning GFCI would do this, but if the GFCI was old and worn it could be opening the contacts slow enough that a detectable arc is being produced.

Determining if the GFCI tripping is causing the AFCI to trip, is a simple test. Simply press the test button on the GFCI. If the AFCI trips, you'll have figured out half the problem. If the ACFI does not trip, you could repeat the test using a receptacle tester with a GFCI test function.

If it's determined that the GFCI is causing the AFCI breaker to trip, replacing the GFCI receptacle may resolve that part of the issue.

Figuring out if the surge suppressor is tripping the GFCI, is a more difficult proposition. It will likely require you to monitor the supply voltage over some time, to identify and document possible surges.

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.