Did/do any commercial passenger aircraft have showers for passenger's use?
On Emirates or Etihad long haul flights, they do have showers available only to certain passengers. Here you can find a link to an article about the showers. After those two airlines, as for inflight showers go, I do not know of any other inflight showers. 
The 777 has inflight showers as well. The airline can request the systems necessary to have the showers. So technically any plane can have it.