Cuba is considered very healthy except for the water; even many Cubans boil their water. That said, some travelers drink untreated water without ill effect. The best solution is bottled water and lots of it, especially for visitors who are not used to the 30+°C/85+°F temperatures. Bottled water (agua de botella) is easily found and costs between .65 and 2 CUC for a 1.5L bottle, depending on the shop. It should be noted that the mineral count (total dissolved solids) of bottled water is quite high compared to elsewhere in the world, so if you are planning to visit Cuba for an extended period of time (e.g. as a student or on work permit), it might be a useful idea to bring a small jug/sports bottle water filter with a few cartridges along to further purify the water.
Cuban milk is usually unpasteurized, and can make visitors sick. Additionally, tourists should be wary of vegetables washed in tap water. Despite the warnings, most Cuban food is safe to eat and you do not need to be paranoid.
The island is tropical and thus host to a number of diseases. Some recommend an aggressive program of innoculations when planning a trip to Cuba, but most travelers come with little or none. Hepatitis B and tetanus shots are recommended by most travel clinics. Hepatitis B is generally spread by direct blood or sexual contact, the innoculation course requires three injections over several weeks, followed by a blood test to determine if it actually worked; shorter courses are available. (Interestingly, the hepatitis B vaccine is actually produced in Cuba for world-wide use). Generally tetanus immunization is more important, since tetanus is a risk with any wound or cut, especially in a dirty, contaminated wound.
HIV/AIDS infection is less than 0.1%, however, as always, you should exercise care and make sure you or your partner wears a condom should you become sexually active while in Cuba.
Cuba has one of the highest number of doctors available per capita in the world (around one doctor for every 170 people), making doctors readily accessible throughout most of the island. Your hotel reception should be able to point you to the closest doctor. (So plentiful in fact are doctors in Cuba, that it is not uncommon to see doctors selling paintings, books or other artwork to tourists at the flea market to make money to supplement their meager salaries.)
Finding medication is, however, often difficult. It is highly recommended to stock up on over-the-counter medications before heading to Cuba, as pharmacies lack many medications that westerners might expect to find, such as aspirin, ibuprofen and immodium. Do not attempt to import psychoactive drugs into Cuba. Havana also features a clinic (and emergency room) for foreigners, which offers extremely prompt service.
Toiletries such as shampoo, conditioner, razors, tampons and condoms are also hard to come across and expensive, so stock up before you leave.