Well, let’s see. I’m doing this from memory, so bear with me.
8 Marlboro cups. These are the ones from the latest catalog - the blue ceramic ones with white speckles?
3 “mugs” - two Christmas ones and one with a flower on it.
6 handpainted china ones that I use for display only in my china cabinet.
17 that match my every day dishes. 17 cups, 8 plates, 11 bowls - hey, someone who was moving gave the whole set to me - I ain’t picky.
7 that are my good dessert china.
5 mugs (beer type) that Mr2U uses as coffee cups.
3 of those car kind - they’re thermos, have a sip top, you know what I mean.
So, if we are talking strictly coffee cups made for coffee, then we have, um, 44. If we are including the kind that Mr2U uses, I’d say 49. Somebody check my math - my calculator batteries are dead. 
As for rotation, I use the flowered one every time it is clean. One of the Christmas ones is used when clean, usually daily, but the other Christmas one, the Walgreen’s or Woolworth’s memorial one, sits on top of the fridge and holds those weird twisty bendy straws my kid loves to use and are a pain in the butt to clean.
The Marlboro ones, the blue and white ones I mentioned, don’t get used that often because they are flippin’ HUGE and my coffee gets cold. But when attempting to annoy me, Mr2U and Mini2U will use them.
The 17 that match my regular dishes get used whenever the Christmas ones, the flower one, the Marlboro ones and the mugs aren’t being used. They are the stupid kind that go with saucers, and are too small to be of any use whatsoever. But Mini2U uses them when he uses his watercolor paints - they are good for holding brush cleaning water.
The other 5 beer type mugs get used for coffee when they don’t have beer in them.
The handpainted china ones never get used. They are looked at but not used. And I have a bad habit of slapping people who get too close to them.
The other dessert china ones get used whenever I have a formal dinner party. The last time was, uh, last Thanksgiving. Of 1999, that is.
Oh - and I have a Dilbert mug at work that I now keep clips and rubberbands in.