Sweden is, on the whole, a safe country to travel in, whether it’s from the point of view of health or otherwise. There are no health risks, but if you’re visiting the country in the winter, it’s wise to pack lots of woolens and an umbrella- the weather can be very cold. In addition, if you’re going off the beaten path- trekking, cycling and so on- take along an insect repellant and stock up on first aid. If you’re on medication, it’s advisable to carry your doctor’s prescription, along with your medicines in their original wrapping. Fortunately, the Swedish medical service is very competent, and you should generally not have any difficulty in finding an English-speaking doctor even in smaller towns.
Crime, especially the sort directed against tourists, is fairly uncommon, but in larger cities, you should take precautions against petty theft. Keep your valuables locked, and stay away from deserted streets after dark.