Austria is a very safe country.
Looking at the homicide rate it is just at 0,6 (/100,000) while the US rate is 8 times higher at 4,8 and European countries like France or the UK have double the rate at 1,1 and 1,2 respectively (source: Wikipedia).
Despite recent headlines that shocked the whole country Austria in general and Vienna in particular remain very safe places to be.
My feeling also as a Vienna resident is one of safety: I never heard of anyone being attacked or physically abused. Women, seniors can walk safely in the streets at night. That however doesn't mean one shouldn't watch for his belongings, because there are pick-pockets, especially in tourist areas. There are also home burglaries. No need to get paranoid but a little bit of common sense will get you a long way: keep your purses tight and always lock your room/apartment when going out.