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SomethingAwful.com published an odd Halloween story Oct. 30, 2001. It's on the front page (and yes, there is one).
It started like this: "In Western Illinois the word "terror" is synonymous with "I-670" or "the bloody interstate". Stretching across the state from East to West, I-670 is one of the most violent and brutal roads anywhere in the world, and not because of traffic fatalities. No, it is said that on the Western end of I-670 a powerful and terrifying beast lurks within the often flooded drainage culvert along the highway."
The ending, no surprise, is depressing and profane, and you'll have to search their site to read it.
I-670 west of I-71
I-670 is another urban interstate with a history and construction cycle spanning many decades. In September 1995, the federal planning document "General location of national system of interstate highways", also known as the "Yellow Book", depicted an inner beltway for Columbus; this would eventually be constructed as parts of I-70, I-71, OH 315, and I-670.
The north leg of the innerbelt was built in the late 1950s and signed I-71. I-70 was to approach the Spring-Sandusky interchange (OH 315/US 33) from the west and then overlap with I-71 northbound through downtown. At that time, there was no concept for I-670; the highway west of I-71 was part of I-70, and the portion east was not yet started. 
By 1965, planners knew that the Spring-Sandusky interchange was insufficient to handle I-70 and I-71 traffic, and a new southerly route for I-70 was conceived.  The "leftover" portion became Interstate 670. Planning for this started in 1965 and finished in 1971. Work was expected to start after the I-70/I-71 interchange was completed in 1976. However, new environmental legislation halted the project, and design was restarted from scratch in 1978. 
Work finished the inner belt section, including the interchanges with I-71 and OH 315. At I-71, the old I-670 passes south of Fort Hayes Army Reserve, while the new one passes north.
I-670 east of I-71
Meanwhile, a freeway leading from downtown to I-270 near the airport was desired, to help develop the regional economy.  Part of this had been built as a US 62 freeway in the mid-1960s. In December 1975, AASHTO approved extending the I-670 designation along this proposed route. 
By 1990, three gaps remained:
All that's left is the paperwork
The AASHTO Standing Committee on Highways (SCOH) Special Committee on US Route Numbering periodically meets to review proposed changes to U.S. and Interstate route designations. The May 14, 2004 meeting covered several routes including the following:
Establishment of Interstate Route 670: Beginning at the intersection of Interstate Route 70 and a new facility under construction in Columbus, then easterly and northeasterly over the facility for 10.7 miles to the intersection of Interstate Route 270 east of Columbus. Now I-670 already existed before this point, but at 9.37 miles; the purpose of this "establishment" was probably to incorporate the new mileage completed in 2003.
In supporting documentation, the FHWA noted it approved the number west of I-71 on Feb. 7, 1975, and east of I-71 on Dec. 19, 1975. 
I-670 Kansas; Missouri
On May 22, 1997, U2 filmed its "Do you feel loved" video on I-670, shutting the highway down for a few hours.