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I-470 (built as non-interstate) Colorado (link)
This state highway/tollway, signed as W-470, C-470 and E-470, is the rebirth ("in state highway form!") of cancelled Interstate 470. Here's some background from Ray Mullins:
"Back in the late(?) 70s, Gov. Dick Lamm redirected the federal funds for I-470 to the 16th Street Transit Mall project. When it became obvious that the SW section of I-470 needed to be built, the feds said "We gave you the funds, you spent them on something else. Tough." So the state built it with its own funds."
The southwest portion of Route 470 was added to Colorado's interstate system in 1968, as a proposed extension of I-225. On May 2, 1969, this was renumbered to I-470; after I-470 was cancelled, the number was withdrawn on on Sept. 20, 1977. 
For more information, see Matthew Salek's Denver's 470 Saga (good history of I-, E-, C-, and W-470)
I-470 Kansas (link)
13.72 miles ; serves Topeka.
The eastern five miles is part of the Kansas Turnpike, which opened on Oct. 25, 1956 . The remainder was already open by 1961. 
I-470 West Virginia; Ohio (link)
10.63 miles ; serves Wheeling metro area. Completed in late 1970s. Why a bypass for Wheeling? Nick DeCenzo writes that I-70 goes through the city and "Wheeling Hill" via a one-lane, height restricted tunnel; therefore a bypass was needed for safety reasons as well as traffic.
On Sept. 12, 1996, I-470 was closed between I-70 (Ohio side) and the Ohio River because of "voids" caused by collapsed coal mines underneath. (470 has since reopened.) 
I-470 Missouri (link)
16.72 miles ; from I-435 in Kansas City to I-70 in Independence. Planned as early as 1970 (14.1 miles, $22.5 million) ; opened between 1981 and 1987.