The MINIs have done extremely well in both NHTSA (government) and IIHS (independent insurance) crash testing. I've had the opportunity to see many MINIs post crash, and the important thing to know is that almost every one of them let the driver walk away with little more than bruises to show for it.
Yes, they're small, and physics can't be broken, however, BMW engineering has made the car as robust as possible, and designed crumple zones to keep the passenger compartment as intact as physically possible. Of note, as of 2009, all of the passive safety & most of the active safety features are standard (including 4 wheel disc brakes, ABS, Dynamic Stability Control, 6 airbags, etc.)
Also, you should be aware of features that help you avoid an accident (aka Active Safety features) such as the responsiveness of the car, power, electronic stability control, and overall size of it (more or less to hit). Having owned 2 MINIs, I can tell you that I avoided several ugly situations because of the immediate response from the steering and firm grip on the road.