I used to try to track this nonsense, but now I'm not sure how. The last time I saw data, the two world leaders were neck and neck -- Father Hesburgh (former Pres. of Notre Dame) and the King of Thailand each had about 125, but that was a couple of years ago. Herbert Hoover (who is no longer collecting them) was a distant third with about 90. I'd love to have current figures for the next edition of Bears' Guide, but I can't figure out how.
http://www.xmission.com/~roconor/Hesburgh_bio.html "His stature as an elder statesman in American higher education is reflected in his 144 honorary degrees, the most ever awarded to a single person." from above link, second paragraph.