This morning our water supply was working fine. Tonight, when we open any hot water faucet in the house, we just get a trickle of warmish water. Cold water is working normally. I checked hot water heater (gas, about five years old); no obvious problem, pilot is working and it kicked in when I turned up temp. A basement tub faucet right by the water heater has the same situation as every other faucet in the house, so I'm thinking it has to be at the hot water heater or the water coming in to it. Thoughts

I'm thinking it has to be at the hot water heater.
And so am I. Lets start with the heat trap nipples, (see image ) if you have them installed. Heat trap nipples are located connected to the inlet and the outlet of the heater. Check and if you have them replace with Brass nipples. If that doesn't get you hot water click on back and tell me. Tom

Do you have a water softener? Is it only supplying water to the heater? Try bypassing the softener or any other filter that is only for the hot and see if you get pressure. You wouldn't have a tempering valve over the heater would you? This is not common but I have seen them in residential applications

do you have a water softener? Is it only supplying water to the heater? Try bypassing the softener
To add to Chayns excellent advice here's a diagram to help you bypass the softener. Turn off the two valves supplying the heater and open up the bypass valve. If that don't get it click on back and let us know. Good luck, tom