First of all, taking the class doesn't necessarily mean you'll be an EMT. First you have to take the exam (preferably the national exam), then you have to be accepted by a department. Finally, you really need to actually spend some time going out on calls for the experience to be worth anything. You will probably only be able to do this in a volunteer capacity, because in order to get paid you usually have to be a career firefighter with EMT training.
Second, no it's not a dangerous job for the most part. Any time there is any violence/danger at the scene, the dispatcher is supposed to have you hold the ambulance a good distance away until the police have arrived. They secure the area before you are asked to move in. The idea is, the police officers have taken a position that involves substantial risk (and substantial training). The same is not true for EMT's (at least according to US national standards), and so they are actually not supposed to be in dangerous situations. Additionally, EMT's can and will be reprimanded for ignoring orders that pertain to their own safety.
The only danger that EMT's frequently encounter comes from psych patients who might be somewhat unpredictable (due to drug ingestion, mental illness, depression, etc.).