My shower and bathroom sink and kitchen sink downstairs don't run any water when turned to hot, but they run cold water. The shower and sink upstairs run hot and cold water. The water heater is downstairs. What is going on? Anyone have any ideas?

If that happened all of the sudden without any renovations being made check if there's a valve along the line that goes downstairs (follow the hot water pipe), you might have closed it erroneusly thinking that was something else... if you did some renovations, well... than you might have done something you shouldn't have...

Fulgur may be new but he makes a good point. Was any repair or installations done recently? A clog in your hot supply that stops this many fixtures doesn't make any sense.