"Think Music" written by "Jeopardy" creator Merv Griffin. According to the official history of the game show, Griffin wrote the "Jeopardy" tune when he invented the show back in 1964.

Here is a cool commercial featuring a 'twist' to the themesong. More back ground from wiki: "Think!" (originally composed as "A Time For Tony" by Griffin as a lullaby for his son) has served the Final Jeopardy! countdown music since the show's inception in 1964 (although it was not used in the 1978–79 version), and is also the melody for the current opening theme. In the United States, it has insinuated itself into everyday communication; the song applies to any situation in which someone is waiting for another to answer a question or make a decision. For example, the theme is often heard at baseball stadiums when the manager goes to the pitcher's mound to discuss a replacement, or at football games during instant replay reviews, or on the Jerry Springer show, a parodied remix is heard when a choice has to be made. A variation of "Think!" was used as a jewelry prize cue, officially called "A Time For Tony," on Wheel of Fortune in the 1980s. Griffin has estimated that the Jeopardy! theme song has earned him somewhere between $70 and $80 million in royalties.[citation needed] The main theme song to the original 1960s version is called "Take 10" and was composed by Griffin's wife, Julann. On the finale episode with Art Fleming in 1975 however, the theme used was "Smile" originally composed by Charlie Chaplin. The main theme to the 1978–1979 revival was called "Frisco Disco" and was composed by Merv Griffin and arranged by Mort Lindsey. "Frisco Disco" would also resurface in 1983 as a prize cue on Wheel of Fortune, and would continue to be used until 1989. The opening theme used was called "January, February, March" also composed by Griffin and arranged by Lindsey, and was also used as the main theme on the first pilot of of the Alex Trebek-hosted Jeopardy! in 1983. (Both themes were composed and released in 1976, two years prior to the revival of Jeopardy! in 1978.) After a second pilot was made with Alex Trebek in 1984, Jeopardy! went back on the air. An electronic version of the "Think!" melody became the main theme, while the original recording was recycled for the Final Jeopardy! Round. The main theme was remixed in 1991 to include a bongo track. In 1997, both the main theme and the "Think!" music were updated, with jazzy orchestral arrangements by Steve Kaplan. The main theme was updated again in 2000, with an arrangement similar to the previous one, but looser and more upbeat. The theme has gone through some slight re-orchestrations since then. The electric guitar-based theme from Rock & Roll Jeopardy! has been used on Jeopardy! leading into and out of commercial breaks during College Championships, Teen Tournaments, and November 2006 Celebrity Jeopardy! episodes. (During a few of those tournaments, it was also played during Final Jeopardy!) Alternate versions of the Final Jeopardy! music have been performed by the UCLA marching band (during the 2001 College Championship), the Yale Whiffenpoofs (during the 2003 College Championship), and organist Trent Johnson during the final Celebrity Jeopardy! show at Radio City Music Hall in 2006. During the show's first trip to New York City, a piano rendition was used. On at least one occasion, the "Think!" theme was not played at all during Final Jeopardy! Before, during, and after Alex Trebek's reading of the Final Jeopardy! clue for show #3985, aired Friday, December 21, 2001, the L.A. Spirit Chorale sang a live, a cappella rendition of "Silent Night", with Clue Crew member Cheryl Farrell performing the solo. This appeared to confuse challenger Carly Minner, who looked up from her podium in surprise when it was announced that time had expired. http://en.wikipedia.org/wiki/Jeopardy%21#Theme_songs