Yes, many aircraft carriers in WWII carried spare planes, though the type and number varied quite a bit by the type of carrier and the individual navy's doctrine (and the availability of spare planes, of course).

For example, Nagumo's carriers at Midway (Akagi, Kaga, Soryu and Hiryu) were nominally supposed to carry three spare aircraft of each type (fighter, dive bomber, torpedo/level bomber) which would have made for nine spare planes per carrier, or another 36 he could have thrown into the fight. (This is not insignificant considering Akagi only had 54 aircraft at Midway.)

The three spare aircraft per squadron were logical for the Japanese carriers to carry, given that their basic tactical unit was the three-plane shotai and that their squadrons air wings were built in units that were multiples of those three-plane units -- Akaki, Soryu and Hiryu each had 18 fighters, 18 dive-bombers and 18 torpedo planes at Midway, while Kaga was similarly outfitted except it carried an oversize unit of 27 torpedo planes.

However, each carrier was down below its normal complement, and the only spare planes carried at Midway were two spare dive-bombers aboard Kaga.