Eight States that have runoff elections
Alabama, Arkansas, Georgia, Mississippi, North Carolina, Oklahoma, South Carolina, Texas
Journal Record, The (Oklahoma City), Aug 8, 2006 Marie Price "Oklahoma one of few states with runoff elections". Journal Record, The (Oklahoma City). Aug 8, 2006....About nine other states have runoff or secondary elections in some form...Runoffs in Alabama, Arkansas, Georgia, Mississippi and Texas are similar to Oklahoma's system....South Carolina's primaries are the responsibility of the parties, but they operate similarly...Oklahoma did away with its runoff system around 1940 but reinstated it six or eight years later.…the early justification was that in the South, where all these runoffs continue to be held, there was a strong one-party system, he said.
http://findarticles.com/p/articles/mi_qn4182/is_20060808/ai_n16660503?tag=artBody;col1 or http://www.accessmylibrary.com/coms2/summary_0286-16302128_ITM
In their system, Louisiana conducts a “nonpartisan” primary election where all candidates participate in a first election. If no candidate receives a majority of all votes cast, a “run-off” is held between the top two candidates. http://www.ncsl.org/programs/legismgt/stateVote/2007_Election_Preview.htm
At least two states have recently repealed runoffs - Florida and Kentucky
April 2, 2008 Kentucky repealed its provision to hold gubernatorial primary runoff elections. “The runoff provision was added as part of election reforms in 1992. The provision only applied to gubernatorial races and was applied if the top vote-getter in each party’s primary election received less than 40% of the vote. The provision was never used but came closest in 2007 when now-Governor Steve Beshear narrowly topped the cutoff by garnering 41% of the vote.”
2001 Florida abolished its runoff primary beginning with the 2002 fall election. “Under the new legislation, the candidate receiving the highest number of votes in the primary election will be declared nominated by their respective party.” http://www.leg.state.fl.us/data/legislators/House/008/Newsletter/2001.PDF