At a fellow cruisemate's suggestion, last May I took a Princess cruise to the Mediterannean. Although they rarely will cut you a deal on a cabin share, I decided to book anyway. I booked a balcony cabin -no share - was just gorgeous and worth every penny. While there weren't a ton of single people. there were just enough to have a great time. The disco (if you're into that) is lively all night long. The casino fun - even if you never gamble - they give free lessons and you can have some fun there with roulette or blackjack, where your $$ can go pretty far.
The jacuzzis at sailaway (aft of the ship), the casinos, the early morning exercise classes (if you're into that) are great places to meet people. Also, the ship sponsors a singles get together the first night on board. Don't miss it. While most of the "singles" were solo travelers, looking for companionship, not romance, I made some wonderful friends and touring buddies that I never would have met if I hadn't gone to the get together. Also, (and maybe I shouldn't say this!) but there's enough testosterone on the ships and a single woman is definitely noticed. I even went back to my room one day and found roses and a bottle of champagne there (from the cabin steward way down the hall!). You'll have all the attention you want (or don't want), as the case may be! I had a great time that I went back in September for two more weeks!! Enjoy - whatever ship you take.