Rekstout is right - Schizophrenia can be broken down into many classification types, depending on symptoms.
Usually the patient has no insight - ie, they don't feel that there is anything wrong or odd about their behaviour or beliefs. It usually takes a third party to notice any "abnormal" behaviour or thinking.
Most schizo syptoms are more of a problem for the patient than anyone else - it is only if they have a psychotic episode that they may become violent to anyone else. The problem with the illness is that once someone has suffered one episode of schizophrenia, they are then more at risk of further episodes. Each time, the chances are that their level of functioning will return to less than it was before the relapse.
Because the person has no insight into the fact that they are ill, they aren't neccesserily motivated to continue to take medication, again leading to increased risk of relapse.
I would also agree with Justawife - when a schizophrenia sufferer is taking their medication, they can be "normal" and lead a balanced and responsible life. However, this relies on them continuing to be motivated to take their medication.