Cuba is generally extremely safe for travelers. Single travelers face no real specific threats or dangers. That said, don't throw common sense out the window. Single travelers -- and women in particular -- should still be careful when walking alone at night, both in Havana and in other more remote destinations.
I have never felt unsafe traveling on my own and there are few other countries in the world, like Cuba, where I would consider taking an illegal taxi with a strange man for hundreds of kilometers down back roads. Remember also that there are severe repercussions for Cubans who commit crimes against tourists.
Perhaps the biggest issue facing single travelers is that of jineterismo, which is a way of life in Cuba. In its most disturbing form, it has become synonymous with prostitution. Sex tourism and prostitution flourish in Cuba, and single travelers of both genders and any sexual persuasion will encounter constant offers for companionship, and usually more. In some cases, the terms are quite clear and a cash value is set. In others, the jinetera or jinetero is just looking for some restaurant meals, drinks, store-bought clothing, food, daily necessities, and sometimes even a good time. Many are looking to cement relationships with foreign tourists that could lead to marriage and a means of improving their standard of living on a long-term basis, either on the island or abroad.
Single women of all ages, in particular, should not be naive about declarations of undying love. You could just be the desperately dreamed about ticket out of the country. Remember that most Cubans are not free to leave Cuba. If you do fall in love, the Cuban government cannot prevent the Cuban from leaving after marrying a foreigner but they make it difficult to grant the correct exit papers (waits of 3 years are not uncommon).