The crime issue is one that seems to get a lot of play in discussions re: St. Louis. It is a concern for me, but I'm also accustomed to the way in which cities work and know that a few blocks can make the difference between a warzone and a beautiful area.
It's my understanding that "North St. Louis" (i.e. the vast majority of areas north of Page Avenue) is what gives the city its tough reputation. If you look at any crime or specifically murder map of St. Louis, you'll find 75-80% of the problems in this area.
Below that, the city appears to be as safe as any other mid-sized American city. There are some pockets of trouble in Benton Park, etc, but by and large there are a lot of very stable, relatively safe areas in "South City:" the neighborhoods of Tower Grove South, Bevo, The Hill, Dogtown, Holly Hills, etc barely have had a murder between them in the last 4-5 years.
As far as I can tell, the area immediately around the college is relatively safe too -- at least Wyndown/Skinker, Delmar, and especially Clayton (which is not in the city proper anyway). Central West End is very close via Metro and is known as a safe, active, and "ritzy" area. Soulard and Lafayette Square are also relatively desirable areas with a lot of artistic activity and relatively cheap housing stock.
This is what I've garnered from a lot of research and a 2-day trip to the city, so don't go all on what I have to say. I'm curious if a currently WUSTL student can agree or disagree with my assertions?