I did the Liberty as a solo/single on 05/26/07. There are not that many solos on the ship but there are plenty of singles. There are family groups, girlfriends travelling together, and loads of mother/daughter pairing.
There are also a decent number of single men on the ship travelling either in pairs or within the aforementioned groups.
If you are looking for a ship romance, I can't give any take on that. However, if you are looking for companionship of a platonic nature, that should be no problem because most of the ship is NOT coupled off.
(cruzin' solo by design)
Freedom ('09), Imagination ('08), Victory ('08), Destiny ('08), RCCL Navigator ('08), RCCL Majesty ('08), Glory ('07), Liberty ('07), Fantasy ('07), Destiny ('06), NCL PofAm ('05), Fascination ('04), Victory ('04), Fascination ('04), RCCL Voyager ('03), Fantasy ('99)