The most popular discount appears to be “on board credit” offered by cruiselines and travel agents alike. Generally you can find these as the cruise is getting closer, so waiting to book could be bitter sweet. You could get a free upgrade if you book sooner, or $50-$100 if you book later. My personal preference would be the free upgrade… since I like to get a balcony and can often get one for the price of a window.
We recently discovered the AARP discount when we booked my dad’s cruise with us last Thanksgiving. I had to call to get the discount, signed him up for AARP (anyone over 50), and he got 5% discount, plus they gave him $50 on board credit.
Many also offer discounts for military, another way to reward our troops.
If you book your next cruise on board, you can often get $100-$200 on board credit for the current cruise. And you don’t have to book a specific date, just place a deposit for a cruise at some point within the next 2-4 years.
I was able to call the cruiseline recently when I saw on board credit and a coupon book being offered for a cruise I had already booked. They were able to give me the same offer, so I was happy 
It’s definitely worth a call periodically to see if you are entitled to any specials or discounts. They are always willing to work with you when they can.