"Run" currently is the word with the most different meanings. The verb-form alone has no fewer than 645 meanings and Peter Gilliver worked for more than nine months to work out all of them.
source NY Times online
Online look at the word
As a child I would read the dictionary,
Yes, I was that kid. I noticed some words filled pages with the different definitions, and once tried to find the word that had the most definitions. It was "ride", with run, set, and put close seconds.
The unabridged dictionaries were the best. I simply looked for pages that were filled with just one words definition, and then calculated by the amount of page space used to determine which word had the most definitions. Not scientific, but fun.
This meant I had to actually look at every page of the unabridged dictionary. Didn't take as long as it sounds.
It was an immature attempt to use evidence based science, to determine which word had the most definitions.