What are some typical chord substitutions in either major or minor keys?

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What kind of substitutions do you mean? In a jazz world? I mean, in jazz you can safely substitute a m7 or m9 chord anytime you see a minor chord (jazzers...correct me if I'm wrong). You can substitute a dom7 chord for a dom7 chord a tritone away.

Is that what you're looking for?

I suppose that you are talking about classical music. In the tonal era (Baroque, Classicism an d Romanticism), the substitutions that were made, are the 2nd degree instead of the 4th degree, and the 6th degree instead of the the 1st degree. So, in C major, for example, in the complete cadence (I don't know any english term for "cadenza", in the harmonic sense), instead of the succession I - IV - V - I, it was possible for the composer to write I - II - V - VI (with a short completion IV, or again II - V7 - I). It's not a rule how the composer substitute a chord with another. It was all about the taste (the aesthetic of the sound).