When you run into someone, you either physically bump against them, or you unexpectedly encounter them. Your bike might run into a mailbox, and as you limp slowly home, you may run into your sister.
If a car runs into a telephone pole, there are bound to be injuries — to the car and the pole, if not to the driver and passengers. But if you run into your best friend from kindergarten when you're visiting Disney World, it's much more pleasant. You can also run into problems or delays: "We're bound to run into difficulties when we try to build the world's largest gingerbread house."