I've seen ten of Strauss's 15 operas on stage, plus a couple of concert performances. My favourites are:
Ariadne auf Naxos (1912/1916)
Die Frau ohne Schatten (1918)
Die Schweigsame Frau (1934)
The other four:
Salome (1905) is sort of OK, but I don't want to see it very often
Intermezzo (1924) is rather bizarre
Daphne (1938) has its moments and I'd like to see it again
And then there's Der Rosenkavalier (1911) which has some nice music but is rather soppy. My favourite character is Baron Ochs!
Oh, and there's a lot of good orchestral music - the one I like best is An Alpine Symphony but the others (e.g. Metamorphosen)are good. And then there are a whole lot of songs (particularly the Four Last Songs) plus several concertos....