Time Out is a pretty unique jazz album that's often overlooked. Most jazz, like rock, is in 4/4 time (with the odd waltz-time tune to liven it up.) Not good enough for Dave Brubeck: Time Out has all kinds of weird compound time stuff going on. Take Five is in 5/4, which gives it its unusual vibe; Three to Get Ready gives you two bars of 3/4 and two of 4/4, alternating (which to me it feels a bit like a car on the verge of starting; I don't actually like that tune.) There's other stuff going on there too but it's been a while since I listened to it. Will dig it out again tonight in his honour.
Non jazz-heads wanting a similar experience could do worse than listen to Money, by Pink Floyd: 7/4 for the verses, then 4/4 for the solo.
Blue Rondo a la Turk is in 9/8 time. But unlike most 9/8 compositions which divide the nine beats into 3/3/3, it uses 2/2/2/3. And smoothly transitions into and out of a 4/4 drum solo in the middle!
If you want to get down with different meters and rhythm you need to check out: Dimi Mint Abba (album: Moorish Music from Mauritania), Afrocuba de Matanzas (find them playing a batarumba), Orchestre Poly-Rythmo (album: the vodoun effect). Lots of others, but those hit all sorts of territories taken together.
Non jazz-heads wanting a similar experience could do worse than listen to Money, by Pink Floyd: 7/4 for the verses, then 4/4 for the solo.