In a Poser animation, can one animated figure control the movements of another, through parenting or other method. For instance, can a human Figure A shake the hand of Figure B, by simply animating the arm and hand of figure A, without having to manipulate Figure B's parts? In essence, one character's movements controlling those of another? I've been trying to figure this out for a while.

 In theory yes, using IK and constraint objects, in practice results can be somewhat unpredictable, when Constraint objects were introduced (Poser 10 I think) they made a tutorial video about them which made it look easy, however as always they "cheated" using Andy an un-skinned character, on regular skinned characters you tend to get weird breaks.at wrist or knee.

Pre-dating the Constraint objects I made this video https://www.youtube.com/watch?v=-2aoquX_CIk&index=69&list=UUEcKgtoS0Z6ryqTwgcioX9w there's a fairly extensive description of my method on the page, again I think it only worked because I was using the mannequin figure and when I re-opened the file some while later it was an irretrievable mess of doggy chew figures.

For hand shake type motions I think it's best to animate both figures as accurately as possible before engaging IK to hold them together 

Ockham had a script for making  multiple figures follow a leaders actions. Not sure if it's still there (ockhamsbungaow.com)  

Thank you so much. I will definately investigate. Cheers.