To begin with, I am a fan of music that has all or most of the following attributes, in no particular order:
High level of musicianship
Complexity (chord progressions, time signatures, harmonic structure, etc)
Broad range of emotional content (positive & negative emotions)
Usually long form (music that develops & changes over time)
Music that bores me, is short songs, in standard time signatures, that follow the usual verse>chorus>bridge format.
The types of music that I like that fit the above attributes are:
Jazz (fusion, avant-garde, post bop, jazz-metal, chamber jazz, M-Base, and other, modern contemporary subgenres)
Classical (20th century from mostly post WWII, contemporary, avant-garde)
Prog (avant-prog, Zeuhl, Canterbury, classic, prog-metal, technical-metal)