Any 22mm band (assuming you have that model) that is thin enough to fit inside the casing (some padded leather bands are too thick to fit) should work. The only thing you may have to do to them is make a cutout (in the center of the band where the pin goes through) but otherwise, the answer is yes. However some bands already have this cutout from the factory.
I know for a fact that the metal bands from the Pebble Steel (around $25-35 depending where you get them) will work just fine, and they already have the cutout I referred to earlier. But if you're looking at a leather or silicone band, and it's thin enough to fit but doesn't have the cutout, you just need to make the modification I mentioned earlier (easiest way is to use your original Moto 360 band as a template).