Overseas travel can sometimes carry the risk of exposure to disease or other health risks. In general it's advised that you stay informed of any precautions or medical requirements for your specific destinations.
Some countries require certain immunizations before allowing entry. In other cases immunization may be requested, but not required. It is always a good idea to travel with a first aid kit containing appropriate medicines and remedies for your specific destination.
Consult your physician before your trip and use the following web sites for accurate updated information:
Travel advisories are issued and updated daily by local governments for the safety of their citizens while traveling.
These may be in reference to political issues, or any specific problems travelers should be alerted to when visiting another country.
While doing your research on safety keep in mind that perspective is relative and ultimate it is up to each individual to determine if a country will be safe for them to visit. Be sure to check as many sources as you can when doing your pre-travel research.
The US Department of State is a good place to start.