The 5th company of the Canadian Queen's Own Regiment was newly armed with Spencer rifles (issued the day before) at the Battle of Ridgeway on June 2, 1866, vs. "Fenian" Irish sympathizers. Some reports say each man was issued 28 rounds of ammunition, others say 40 rounds per man. I suspect they carried 28 rounds and left the rest with their baggage, as sources report the Canadians left their ammo reserve at the train station. Soon after clashing with the Fenians at Lime Ridge, the 5th company began to run out of ammo and had to be replaced in the line by other companies armed with muzzle-loaders (who either had more ammo to begin with or who did not expend it as fast). I'm not sure how they carried their cartridges, but if 28 (or 40) rounds per man could be expended in a brief clash of arms, an experienced Spencer-armed soldier would probably have carried more.
With U.S. troops in the Civil War, who often had much more than one day of experience using their issued Spencers, I suspect a cartridge pouch carrying 20 or so rounds was the immediate ammo source while fighting and, as Cannonman1 suggests, that extra rounds were carried in pockets and haversacks. I also agree with Blair that saddlebags or other saddle-mounted pouches were likely used by cavalry to transport ammo, but for the actual fighting, much of which cavalrymen did dismounted, they probably carried extra rounds on their person in pockets, bags, or haversacks.
--DJ