The answer is: "2000" -- at least for oceanic operations.

I just ran across AC 91-70B -- Oceanic Operations, dated 09/06/94, at
http://www1.faa.gov/fsdo/orl/files/advcir/AC9170B.TXT.

Chapter 2, OCEANIC OPERATIONS FOR ALL AIRCRAFT IN ALL GEOGRAPHIC AREAS, par
6.e(4) states:

(4) ICAO Documents 7030, "Regional Supplementary Procedures"
and 8168, "Aircraft Operations Volume I," state that
transponders shall be operated as follows:

(a) when the aircraft carries serviceable Mode C
equipment, the pilot shall continuously operate in
this mode, unless otherwise directed by ATC;

(b) in NAT airspace, unless otherwise directed by ATC,
pilots shall retain the previously assigned
transponder code for a period of 30 minutes after
entry into the airspace, then operate on code 2000;

(c) in oceanic airspace other than the NAT, pilots shall
operate the transponder and select modes and codes as
directed by the ATC unit with which the pilot is in
contact; or

(d) in the absence of any ATC directions, pilots shall
operate the transponder on Mode A Code 2000.


Further, in Chapter 3, par 9.g, discussing non MNPS airspace over the Atlantic:

Navigation equipment adequate for operation in accordance
with the flight plan and with ATC clearances shall be
carried. SSR transponders with Mode 3/A and C are required in
Iceland. Pilots shall operate SSR transponders continuously
on Mode A, Code 2000. Departing aircraft shall retain the
last assigned code for 30 minutes after entry into NAT
oceanic airspace unless otherwise instructed by ATC. This
procedure does not affect the use of special purpose codes
7500, 7600 or 7700 when required.


Chapter 4, par. 4.g (Northern Pacific ops):

g. Transponder Codes. When operating west of l64E, transponders
should be set to Mode A Code 2000. When east of 164E, a
discrete code may be assigned. This code should be maintained
unless otherwise advised by ATC. If no discrete code is
assigned, transponders should be set to Code 2000.


Chapter 11, GENERAL AVIATION SHORT-RANGE AIRCRAFT OCEANIC OPERATIONS, par. 2.j,
says this about transiting Iceland:

Navigation equipment adequate to navigate in accordance with
the flight plan and in accordance with ATC clearances will be
carried aboard the aircraft. Secondary surveillance radar
(SSR) transponders with Mode 3/A and C are required in
Iceland. Pilots shall operate SSR transponders continuously
on Mode A, Code 2000, except that departing aircraft shall
retain the last assigned code for 30 minutes after entry into
NAT oceanic airspace unless otherwise instructed by ATC.