I think for me I listen for song structure first and foremost. It can be any genre of music and if I like the song structure there's a good chance I'll like the song.
Secondly, I like a good performance, it trumps sound quality of a recording, though I like to have both if possible.
Then I listen for instruments, hard rock for example, catchy guitar riffs, good bass, vocals, drumming, etc.
I try to follow all the instruments at the same time so if the song is good I'm in my bliss. Sometimes I focus on just on one instrument, guitar, bass, drums, keyboard.
With trance/electronic I'm listening for creative music themes and sounds.
And if I'm in the mood I want the music to sound powerful.