Travel is broadening and people should travel as much as possible. It gives you a different perspective on life, people, history and the world in general. People really need to see as much as possible. That being said there are some countries that are not very safe to travel to or through. The problems can be social, political and religious or even something in the way of a natural disaster!
Social problems primarily include crime, it some areas and countries it is rampant. If they see a visitor from another country, they can and will try to capitalize on it. Where is crime currently high enough to avoid a country? Haiti is one such place. There are virtually no tourists that travel to Haiti that are not victimized in some way. Fortunately, most of the crime is petty theft, for a high murder rate, the Honduras rates number one closely followed by Venezuela! That does seem to be shifting in recent times, but travel in areas with high shooting incidents are not safe for travel!
Political and religious situations can make a country unsafe for travel by specific nationalities. For instance Iran would not be a safe place for Americans to visit and Israelis should probably avoid Syria if possible. Pakistan has never been safe for most people from India. China is now getting better, but for decades it was unsafe for most westerners to travel there unless on business. Politics can change quickly, as they are in China, but most of these are unsafe for religious reasons and that takes a long time to alter. Look carefully before traveling into any place where religion is extreme!
Then there are natural disasters than can make a country unsafe for travel. This can best be seen with the recent earthquake activity in Haiti. It has leveled and damaged buildings and tremors continues, so even solid accommodations may not be truly safe. Also there will now be health concerns from the tragic loss of life, spreading of disease and contaminated water supplies. You can also look just to the south and east at the Caribbean Island of Montserrat, an exploding volcano. Safe? Relatively, though the volcanic ash has been shown to cause respiratory problems!
Are there other countries that are not safe for travel? Certainly! Just try to Google the topic and see what comes up!