This is the one that always comes to my mind:
Herman Talmadge (1957-1981) -- defeated for re-election
Mack Mattingly (1981-1987) -- defeated for re-election
Wyche Fowler (1987-1993) -- won a plurality in November 1992, but defeated in run-off
Paul Coverdell (1993-2000) -- re-elected; died suddenly at age 61
Zell Miller (2000-2005) -- appointed, then won special election; did not seek election to full term
Johnny Isakson is about to become the first person in decades to serve two full terms from this seat
Isakson might resign due to Parkinson's disease.
Missouri, Class 1
John Ashcroft (1995-2001) - retired and appointed US Attorney General
Jean Carnahan (2001-2002) - appointed to replace her husband, Mel Carnahan, who was elected to the seat in 2000 but died in a plane crash before he could take office; defeated when she ran for election
Jim Talent (2002-2007) - won against incumbent Jean Carnahan; defeated in 2006
Claire McCaskill (2007-present) - elected 2 times; might lose in 2018