Should I replace my 36 year old copper house wiring with UF-B?
In most locations, at least in the US and Canada, houses were wired in 1982 with NM cable (Romex) very similar to the NM used today.  That stuff seems to be holding up pretty well, except where it's exposed to excessive heat, sometimes in a light fixture.  But I don't know anyone that says that that wire is due for an update.  

If you want to replace anything, your panel and breakers would be the first thing I'd consider.  Breakers do have a limited life span, and if you're going to replace the breakers, it may or may not be worth replacing the panel too - something to look at.  

If you have money to burn and just really want to upgrade your wiring whether you need it or no, without question, I'd go with EMT conduit.  That would be a huge job but conduit is forever.  If you find a buyer that appreciates a good overbuilt system it may add value to your home.  It sounds excessive to anyone from anywhere else, but all homes in Chicago are done in conduit.  I have come across a few small apartment buildings / triple-deckers done in conduit.  If you want to go even further into eccentric multimillionaire territory, you could do it all in rigid conduit, but that could cost more than the house.  

If you're going to overbuild a bit and go with conduit, I bet you'll also want a bolt on panel.