I have a bunch of A15 ceiloing fan bulbs. Are they supposed to fit fixtures that take an A19 bulb?

Lamps, (light bulbs) incandescent bulb diameters are measured in 1/8 of an inch increments.

The number "15" tells us that the lamp is 15, 1/8ths of an inch in diameter or 15/8 =1-7/8 inches.

An A19 is 2-3/8 "

An A15 lamp will fit in a fixture rated for a A19, but not the other way around.

Bulb diameter. Bulbs are measured in increments of 1/8".....a "15" is 15/8th's, a 1"19" is 19/8th's
Easiest way to look at it is with flourescents... a T-8 is 1 inch (8/8) a T-12 is 1 1/2 inch 12/8

Adding to what the others have said, just make sure you are not exceeding the wattage rating (usually 40 or 60 watts per socket with fans) and you should be set.