I teach physics for princeton review and from everything I have seen, only two constants need to be known from memory: g and c.
g = 10 m/s^2 (good enough approx. like Brett said)
c = 3 x 10^8 m/s
any other constants need not be known from memory, although it doesn't hurt to remember any extra ones you may use, such as coulomb's constant (9x10^9) or the elementary charge e (1.6x10^-19). It would save you the time of searching through a passage to retrieve them, as they would be given.
As far as gchem, when I studied I remember memorizing only avogadro....no potentials or heats of formation or any of that. Oh that and the heat capacity of H20 is 1 cal/g*C. I think that was it.