Just to clarify a couple of points mentioned above.
For drinks priced more than $ 10.00, there is a 25% discount with the cheers program, rather than paying the amount above the $ 10 limit. Those drinks count against the 15 per day limit.
Sodas and non alcoholic frozen drinks do not count against the 15 drink limit. The limit is 15 alcoholic drinks.
If you get on the ship and go straight to the bar to get a welcome drink and your cheers sticker, you will be charged tax on any drinks purchased while you are in a US port, but not on the cost of the cheers program itself.
dsgbill's post above is very helpful in figuring whether cheers is worth it for you. If each person in your cabin averages 7 to 8 drinks or more per day, you'll save some money. More importantly, with your drinks paid for, you won't be worrying about how much the drink costs, as long as it's under $ 10. You'll just order what you like.