Cuba is generally a very safe country. A certain degree of common-sense and caution is advisable, especially in major cities. The police force, which is referred to as "Policía Nacional Revolucionaria" or PNR is then expected to provide help.
Tourists are generally advised not to involve themselves in the following three areas: politics, drugs, or pornography/prostitution. It is advisable not to make any such comments.
However, a few well established scams exist:
Insurance price for the rental cars. It is quite expensive as you may get to pay twice the real cost. You should keep in mind that there is one type of insurance policy covering everything (except for radio and tires) and the price varies only depending on the car type.
Fake cigars. Make sure you buy cigars in official shops, do not trust the tobacco factory where the tourism guide takes you to.
"Friendly" locals inviting tourists to bars for a drink or to a restaurant; the tourist will be charged two to three times the normal price, and the spoils split between the establishment and the "friend".
Water is often sold around tourist areas. Sometimes these bottles have been filled with local tap water and re-sealed. You can usually see this tampering on the bottle, but not always, in any case tap water will taste markedly different to bottled water and should be avoided in all cases.
Money scams. Do not let your credit card out of your hands, and watch as the salesperson passes the card in the machine. Merchants in small shops may take your card to an adjacent bank counter and use it to take out a cash advance. In Havana it is important to always be careful when using money. When taking a taxi, many drivers will try to set an artificially high fare before departing. If in doubt, insist that they use the meter.
Cuba is considered very healthy except for the water. The best solution is bottled water and lots of it. It should be noted that the mineral count 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, 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.
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.
Emergency number: 106