Longest Filibuster in modern history was about 24 hours in 1957 by Strom Thurmond.
Two of the top five are from the 80’s. Wayne Morse, my ideal Senator, (I grew up in Oregon) holds the number three spot with 22 hours and change.
http://usgovinfo.about.com/od/uscongress/tp/Five-Longest-Filibusters.htm