Meet or find by chance, as in I ran into an old friend at the concert. [c. 1900]
See run against, def. 1.
Collide with, as in The car ran straight into the retaining wall. [c. 1800]
Incur, as in We've run into extra expenses with the renovation, or James said they've run into debt. [c. 1400]
Mount up, increase to, as in Her book may well run into a second volume.
Follow without interruption, as in What with one day running into the next, we never knew just what day it was! or He spoke so fast his words ran into one another. [Late 1600s] Also see run into a stone wall; run into the ground.