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We mean it, man
Though I-40 ends at I-15 in Barstow, Calif., state route 58, much of it freeway, continues to Bakersfield, then I-5. Extending I-40 along 58 would almost be a slam-dunk. In fact, this stretch of road was submitted for inclusion in the Interstate system on August 8, 1956, but was turned down.
For more about CA 58, see Dan Faigin's California Highways
16.22 miles ; west from I-40 to I-44 in Oklahoma City. The part between I-35 and current I-44 was already done in 1965. A loop along current US-44 up to OK 66, then east to I-35 again, was a planned extension of I-240, for a total of 31.76 miles. 
Dylan Wilbanks writes:
"I-240 used to run from I-40 west through Moore, then turned north along the current I-44 around the city and then across the north along Grand Avenue. Until around '82, the Grand Avenue stretch east of US 77 was nothing more than a wide boulevard -- complete with traffic lights where the road to the zoo (Kelley Ave) intersected. Ten endless years of construction, during which I-44 was extended from the Turner Turnpike gate to Wichita Falls along existing roads, put an end to the traffic signals and I-240 as Grand Ave." 
19.27 miles ; southern loop of I-40 in Memphis. Dates back to 1962 or earlier.
This was to have been a 30.8-mile beltway, but the planned segment of I-40 straight through downtown was cancelled, and I-40 was routed along the top half of the loop. 
In January 1955, a consulting firm drew up plans for Memphis' freeway system, including I-240, the Overton Park route, and an interstate freeway, never built, that would have connected I-55 and the northwest section of I-240 via Riverside Drive and Mud Island.
In fall 1957, residents collected 10,000 signatures protesting the Overton Park route, after plans were shown in the spring. In early 1960, the Chamber of Commerce pushed completing the park freeway before I-240, to help keep business in the city.
On April 5, 1968, the city council approved the I-40 segment as "feasible and prudent". On April 19, Administrator Lowell Bridwell reconfirmed Federal approval of the proposed route, and on Nov. 5, 1969, US Secretary of Transportation John Volpe approved the plan, and the state bought the right-of-way.
A month later, a conservation group filed a lawsuit in federal court to halt construction. On March 3, 1971, in a decision written by Justice Thurgood Marshall, the Supreme Court ordered reconsideration of the Overton Park decision, which mandated that I-40 be shifted to the northern beltway. This decision became a precedent for similar cases and the interpretation of the "prudent and feasible alternative" requirement of Section 4(f) of the DOT Act. (Section 15 of the Federal-Aid Highway Act of 1966, approved September 13, 1966, adds a similar provision to Title 23, United States Code, as Section 138, "Preservation of Parklands.") 
In the 1970s, TDOT proposed tunneling under the park; but 1980, however, expressway supporters had given up, and opted for trade-in funds instead. The I-40 segment through Overton Park was deleted on Jan. 26, 1981.
See also: Memphis Freeways (Michael Adams; maps of historical and proposed freeways)
I-240 North Carolina
9.14 miles ; from I-26/40 to I-40; Asheville. Originated in mid-1970s. (If "Asheville" isn't a terrible pun for a town in a tobacco state, I don't know what is.)
2 extra lanes in West Asheville proposed
To address increasing traffic in the area (along with an extension of I-26 to the north), NCDOT in May 2002 unveiled a plan to widen I-240 from four to eight lanes. This plan was earlier announced in 1998, but withdrawn for further study due to community opposition.
The widening is part of a project extending from the I-40/240/26 interchange to a planned bypass of the Smoky Park Bridge. Substandard interchanges at the bridge cause problems; for example, if you miss a sharply curved ramp to I-240 west, you end up on city streets. 
What happens if I-240 is not widened?
A traffic consultant stated that if I-240 is left at four lanes, the average speed would be "a hard walk" in 2025.  In addition, since the northern I-26 extension will use the portion of I-240 included in the project, FHWA has required that the road be brought up to current interstate standards. Otherwise, the extension cannot be called I-26.