I've always been of the opinion that the majority of people who commit the most serious violent crimes are suffering from mental illness in some form or other.
This shouldn't be taken as a connection between mental illness and violence as I also think that most people with a mental illness don't commit crime and aren't violent, but rather that most people who have committed a serious crime are mentally ill.
Just taking Peter Sutcliffe as an example, how can it possibly be argued that somebody who has done what he did be anything other than mentally ill? In my mind 'sane' people don't go hitting women round the head with a ball pein hammer.
This is only my opinion, and I'm not posting to cause offence to anyone who has had any experience of violent crime, but I'd be interested to hear what you think?