How does one know when it's time to get the rear hub serviced or replaced? I'm not sure how freely it should spin, since there's a bit of resistance with the chain and the rest of the drive system. Front wheel hub seems fine right now.

Too bad you're in Peoria - otherwise I'd say "stop by".

First - it depends on the hub. Some simply are not readily serviceable.

Remove the wheel from your frame. Hold the axle ends - 1 in each hand - and spin the wheel. If it spins smoothly then you're fine. If it's crunchy, grindy, sandy, ticky, etc. then you have an issue. Could be as simple as a hub adjustment. Could be as complex as an overhaul or hub/wheel replacement.