The Columi piece at the end of a HM FP, the columi and Rakata pieces in Lost Island, and Rakata pieces in operations only for the classes present, always. Anyone saying otherwise, prove it, because I've done literally hundreds of HM FPs and never seen a single columi piece drop from the final boss that wasn't for one of the classes involved.
Everything else I'm not sure.
I've helped gear fresh 50 sorcs by running even HM FP with a sin tank, two sorc dps, and sorc healer, because the inquisitor piece is guaranteed to drop from the last boss.