16 colors, technically. But only four at a time, and three of those were selected from two preset palettes, both of which were hideous (one green/red/brown, one cyan/magenta/white).
I remember the palette choices in CGA were downright bizarre; they'd be 4 colors that you couldn't possibly use to make anything look right. At the price of the card and the display, you're like "wait ... that's it?"
[0] Ignoring all of the interesting things coming out of the 8088 demo scene, nothing that I'm aware of from the 80s was capable of anything close to that.