Stop because of lack of power or force, as in The alarm clock finally ran down. [Mid-1700s]
Make or be tired, cause to decline or be declined in health or vigor, as in His long illness ran him down, leaving him with no energy, or After that huge assignment his strength ran down. [First half of 1800s]
Collide with and knock over, as in The speeding motorist ran down a pedestrian. [Second half of 1500s]
Chase and capture, as in Police detectives ran down the suspects. [Second half of 1600s]
Trace the source of, as in She ran down all the references at the library.
Disparage, as in Don't run him down, he's a talented actor. [Second half of 1600s] Also see put down, def. 4.
Also, . Look over, review, as in Let's run down the membership list again and see if we can pick a delegate, or She ran her eyes over the crowd, looking for her husband.
In baseball, tag out a runner between bases, as in We might have won but in the last inning they ran down two of our runners.