I called BA and they told me that pretty much all fares for many of the carriers apply. To be specific, the following codes accumulate miles:

AA: C,S,Y,B,G,H,I,K,M,N,O,Q,R,V,A,W,X,Z
CP: J,C,B,G,H,K,M,N,O,P,Q,V,X,Y,Z
CX: J,C,D,I,W,B,Y,H,M,V,T,K
AY: C,S,Z,A,B,G,H,K,L,M,Q,T,U,V
IB: J,C,D,Y,M (the cheapest)
QF: J,D,C,B,I,K,L,M,Q,T,U,V,W,Y,N(INT'L ONLY)

On BA, the only fares that don't qualify are H,G,and Z.

Obviously, all AA/BA trans-atlantic exclusions still apply.