The longest completed pass in the NFL (who cares about attempts, really?) is 99 yards, by the following QB's on the dates listed. (http://www.nfl.com/history/randf/records/indiv/passing)
Frank Filchock (to Farkas), Washington vs. Pittsburgh, Oct. 15, 1939
George Izo (to Mitchell), Washington vs. Cleveland, Sept. 15, 1963
Karl Sweetan (to Studstill), Detroit vs. Baltimore, Oct. 16, 1966
Sonny Jurgensen (to Allen), Washington vs. Chicago, Sept. 15, 1968
Jim Plunkett (to Branch), L.A. Raiders vs. Washington, Oct. 2, 1983
Ron Jaworski (to Quick), Philadelphia vs. Atlanta, Nov. 10, 1985
Stan Humphries (to Martin), San Diego vs. Seattle, Sept. 18, 1994
Brett Favre (to Brooks), Green Bay vs. Chicago, Sept. 11, 1995
Trent Green (to Boerigter), Kansas City vs. San Diego, Dec. 22, 2002
Jeff Garcia (to Davis), Cleveland vs. Cincinnati, Oct. 17, 2004