Considering the large number of people visiting Oxford, the city remains reasonably safe.  However, pickpockets are always operating in busy areas, so beware.  Also, you should be aware of the area around the coach station and George street, especially late at night.  The area around the Cowley road can also be tricky at night.  There are also other parts around the suburbs which are particularly dangerous at almost any time, but a tourist would need to willingly transport himself to such places, so there is little point in giving additional details.  Generally speaking (and this is very general) the area around the north of town is the safest, while the south east is the least.  For the most part adopting the same precautions as in any major tourist areas should allow you to have a trouble free stay.