Amy Shira Teitel of Vintage Space shares lots of cool facts about the golden age of space exploration. Here, she enumerates the engines (and motors) it took Apollo to get to the moon.
And for the nit-picky, she has even more specifics about the count. From her Discover article:
If you're keeping track, that's more than 83 engines and motors; you might have counted 87. There were actually 88 on the Saturn V, but five did nothing during an optimal mission. The four motors that powered the Launch Escape System were aided by a pitch motor that would direct the escaping Command Module safely away from the exploding rocket. Those never fired so I left them off my count.