Roll Call's Top Ten
1961 Texas Senate race: John Tower (R) vs. William Blakley (D)
1970 Tennessee Senate race: Al Gore Sr. (D) vs. Bill Brock (R)
1974 Nevada Senate race: Paul Laxalt (R) vs. Harry Reid (D)
1980 Idaho Senate race: Frank Church (D) vs. Steve Symms (R)
1980 New York Senate race: Al D’Amato (R) vs. Elizabeth Holtzman (D)
1984 North Carolina Senate race: Jesse Helms (R) vs. Jim Hunt (D)
1992 Georgia Senate race: Paul Coverdell (R) vs. Wyche Fowler (D)
1994 California Senate race: Dianne Feinstein (D) vs. Michael Huffington (R)
1994 Virginia Senate race: Chuck Robb (D) vs. Oliver North (R)
2004 South Dakota Senate race: Tom Daschle (D) vs. John Thune (R)
I'd agree with 2004 SD, 1984 NC, 1980 NY, 1970 TN, and perhaps 1961 TX, but in lieu of the other five, I would include the following:
--1964 NY. Along with Helms/Hunt, the only Senate race during this time period that overshadowed the same year's presidential contest. This race had everything: personal intrigue between LBJ and RFK; the typical ethnic, racial, and regional squabbling among the NY Democratic Party; Kenneth Keating's debate against a chair, after the Keating staff blocked RFK from entering the debate hall; an outcome that positioned RFK to eventually rival Johnson for control of the Democratic Party.
--1970 NY. A three-way contest between Republican Charles Goodell, appointed to the seat following RFK's assassination; Richard Ottinger, an early environmentalist and ardently anti-war Dem congressman; and the Conservative Party nominee, James Buckley (brother of the National Review founder and editor, William F. Buckley). Goodell's lurch to the left in the Senate robbed him of much Republican support, and it appeared that Ottinger would edge Buckley until Spiro Agnew made a highly-publicized visit to the state lambasting Goodell (whom the VP denounced as a"political Christine Jorgenson"). As the White House had hoped, Agnew's attacks triggered a sympathy vote for Goodell among the principled voters of the New York City Left, who switched from Ottinger to Goodell in just a large enough number to ensure the election of Buckley with 39 percent of the vote.
--1986 SD. A race that matched the state's leading political figures of a generation: incumbent Republican James Abdnor, who had crushed George McGovern in 1980; maverick then- and future governor (and congressman) William Janklow; and then-congressman Tom Daschle. Abdnor edged Janklow in the primary but could not best Daschle in an outcome that previewed the Dem recapture of the Senate in 1986.
--1992 IL. A case could be made that this contest featured the biggest Senate upset of the last 50 years: in 1991, who could have predicted that incumbent senator Alan Dixon, overwhelmingly elected in 1980 and re-elected in 1986, would fall in the primary to a black woman who had never run statewide? Though her Senate career didn't live up to the promise of the campaign, Carol Moseley-Braun's victory in many ways set the stage for the (slowly) increasing number of African-American candidates making realistic statewide runs across the country.
--2000 MO. Another clash of state political titans, pairing former governor and then-senator John Ashcroft against then-governor Mel Carnahan. Carnahan's death in a plane crash seemed to seal the race for Ashcroft, only to see his widow, Jean, announce that she would accept the seat in her late husband's place.
And, perhaps replacing Texas 1961 would be North Carolina 1990, if only because it featured the most famous Senate campaign commercial of the last 50 years--Jesse Helms' brutally effective "white hands" ad, used against the African-American mayor of Charlotte, Harvey Gantt.