I have a Masters in Physics with Space Technology, and I am just (4-5 months) about to finish my PhD in Quantum Physics. One possible career would be to continue as a researcher, although ensure you have a real passion for the subject, it can get quite hard in research.
Other people I know who have an astrophysics degree have gone into banking, one now pilots 737's for easyjet, another is a teacher, another started his own job. Physicists are generally well renowned for being good at problem solving (and numbers), so lots of jobs are extremely suited.