I don't make a conscious effort to save money when I'm onboard but the things that do save us money are:
1. Pre-buying in cabin bar set up. Buying a bottle for even $80 is less expensive than the cost of that number of drinks. Carnival has the least expensive in-cabin bar setup with many bottles of spirits around $40. Celebrity is the worst with costs around $100/bottle.
2. Taking on your own allowed wine. Two bottles of wine can save a few dollars.
3. Booking or doing your own shore excursions. I have always had better results, seen more, had more fun and spent less money when doing private excursions rather than the ship's excursions.
4. Not buying photographs. We have bought a few over the years but it is not something we normally do. There have been cruises where we haven't even went to look at them.
5. Get OBC from your travel agent, shareholder credit or booking incentive. Always ask your agent if they can sweeten the deal with OBC. Do this before you book because you may not get it later. If you have cruise line stock then take advantage of the shareholder credit. Buying 100 shares just for a $100 OBC isn't a great idea but if you have the stock in your portfolio or purchase it as an investment then you should take advantage of it. Look for bookings that give you OBC incentives. If the price is good and they are giving you OBC then it's just a better deal.
6. You can always smuggle booze. If you are caught you will have to face the embarrassment of having to go to the "Naughty Room" and get your luggage but you won't be kicked off the ship for trying. I don't condone this but it will save some money.
7. Set a realistic per diem for expenditures and stick to it. Don't set your budget so low that you feel you are depriving yourself but set a budget you feel you can live with and enjoy yourself.