I'm going to throw the concept of the clave into the mix. Clave (or key) has it's roots in african music, but is most well known in latin american music in the son clave or rhumba clave. These are repeating subdivisions of a duple or triple based meter (generally 2 bars of 2/4 or 6/8) that form the rhythmic foundation of popular cuban dance rhythms like the mambo, rhumba, son, songo, timba, etc. The clave serves as a framework for the rest of the instruments to hang from and syncopate rhythmically.
It can also serve as a pivot for subdivision modulation between duple or triple, as demonstrated here by Horatio Hernandez:
And if that's too didactic for you, check this video of him solo on the kit, maintaining the rhumba clave on his left foot almost continuously through various subdivisions, permutations, and choppy nuttiness on top. Left foot clave starts around a minute in and warning, the is at a drummers festival so it gets pretty showy:
I find as I grow older that I'm less interested in chop-heavy, count the numbers heavy prog or math music (as has been mentioned by earlier posters). The most interesting odd signature (or perhaps non-duple) music is that which has an inherent groove that you can feel and potentially dance to (or at least allows you to entrain, even if bodily motion ain't your thing).
A clave can serve to anchor the groove and your orientation within the meter. To wit, check out this Mehldau trio recording of All the Things You Are in 7/8:
the clave here is 4+4+3+3, and you can hear it anchoring all of the phrasing, solos, etc. throughout the tune.
Once you practice a particular meter/clave enough, you can begin to feel that underlying rhythm, stop counting, and start really playing in the meter, be it 4/4 or 11/16.
And for some gratuitous and showy both extreme mathy-ness and feel in one song, the Bad Plus is a bit of a guilty pleasure: