All right, I'll bite.
I listen to a lot of jazz and swing, as it's one of the musical genres I actively perform. Within jazz, it's changed hugely in the past hundred years (aka its entire existence). Personally, my favorite era of what we call "jazz" is right where "Sing, Sing, Sing" belongs, where jazz was dance music - and pop music! - and big bands like Glenn Miller's, Benny Goodman's, Tommy Dorsey's, etc. ruled the day. The Stan Kenton Orchestra, which came at the end of that period, is (usually) my favorite big band. After that, jazz began the shift from dance music to art music with the advent of bebop - and that's where I stop being interested. Granted I hear and perform bebop on a regular basis because that's the prevailing style amongst jazz musicians here, but most of it lacks what I love about jazz. The great bebop players like Charlie Parker and John Coltrane are unlistenable to me. Just fast notes upon fast notes upon fast notes...at a certain point it just becomes noise, and however genius their harmonic vocabulary is (and it is often very genius) the music is gone in my opinion. I can dig the "Cool School" (Miles Davis, et al), which is a lot slower and more subdued, but it's still not something that I listen to for fun. Continuing on chronologically, some post bop stuff I do like. Some hard bop brought back rhythm-oriented (rather than lick oriented) jazz, and the introduction of Afro-Cuban influences around this time spawned one of my very favorite forms of music, Latin jazz. Nowadays there's a lot of contemporary jazz I really don't like, but a lot that I do - especially Japanese jazz fusion (but that's another tangent altogether).
It's hard to say what my overall favorite era of music is because it really depends on what genre. Classical is another genre I'm heavily involved in, and my favorite period of classical music is the Romantic period, which includes composers such as Wagner, Debussy, Rachmaninoff, Tchaikovsky, Bruckner, Strauss, and Mahler. However, I also really like the Baroque (particularly Vivaldi), and earlier (such as Gabrieli and Josquin des Prez). Josquin, who lived from the late 15th to early 16th centuries, wrote achingly beautiful sacred music, including a moment in one of his masses that I believe to be the best moment in all of Western music.
If we're talking rock, my favorite era would be the '70s and '80s. Lots of good stuff happening of course, but particularly prog rock and my favorite band (the Alan Parsons Project) were around then so that's the main draw for me.
There does happen to be stuff from the 21st century that I like, though. Eurobeat is a guilty pleasure of mine and I love it to death (definitely my favorite "pop" genre and one of my favorite genres full stop), and I also very much enjoy early 2000s trance. Finally, contemporary film and video game soundtracks make up a large part of what I listen to.
Sorry for the long post, but...you got me talking about music.
I might throw together a Spotify playlist eventually.