Typhoid is a problem in some areas of Morocco and Turkey, and Malaria is returning in Southern Italy. Contact your doctor if you are concerned about these. Aids, and other std's, are prevalent all over the world. Practice safe sex. If you have medical needs, like diabetes, get a letter from your doctor and prescriptions that you can use in Europe.
Associations dealing with specific medical problems can help.
If you do get sick try a local pharmacy, if it is serious your embassy , local consulate, or tourist office can provide an english speaking doctor. Hopefully you will not be in a situation involving the police, but if you are always ask to contact your embassy, they can provide advice over legal matters. Most areas are safe, avoiding dark streets, travelling alone and looking wealthy should keep you out of trouble. Keep your money in a money belt, and try not to carry allot of cash. Watch out for pickpockets especially in train stations and lock your luggage.