I did a bit of an experiment. I found the complete text of Obama's national security speech from last week. Using the control-f function on my browser, I discovered that the man used the word "I" 108 times in that speech. As rendered [sic] by the NYTimes, the speech was 8+ pages--let's call it an even twelve times per page that the man said "I".
I'm reliably informed that his speech lasted 60 minutes. That's 1.8 times per minute, or one "I" every 33 seconds.
I believe that must be a record for an American president. Can anyone think of a speech that would top it?