From this list:
STS-41-C (launch) / STS-32R (retrieve): LDEF
STS-41-B (launch) / STS-51-A (retrieve): Palapa B-2 and Westar 6
STS-46 (launch) / STS-57 (retrieve): EURECA
H-II Test Vehicle 3 (launch) / STS-72 (retrieve): Space Flyer Unit
That's fewer than I expected. There were some on-orbit repairs where the satellite was redeployed after the repair.
Let me supply the "why" part from what I found --SF.
LDEF from NASA was more of a container than a satellite in the classic sense; its purpose was to expose a multitude of material samples to space for a long time; recovery was necessary to perform analysis of the samples and how they fared in space.
Both Palapa B-2 and Westar 6 were commercial communication satellites, that ended up in wrong, useless orbits through their boosters misfiring. They were recovered for refurbishing, resold to other parties and put in orbit again, where they serve just fine. (in case of Palapa insurance reasons might have played a role, but I'm not exactly clear as to, how).
EURECA was an European unmanned laboratory, many of its experiments involving material engineering (also, biology). It was recovered to collect the results (products) of the experiments and to be refurbished and resupplied with a new batch of experiments for relaunch (which never happened).
Space Flyer Unit was another laboratory, this time launched by Japan, but containing experiments valuable to NASA and American organizations and corporations. It contained some material engineering related experiments, and one biology-related (hatching an egg). Retrieval of products of the experiments was required.