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"We thought Peoria already had a pretty good road to Chicago..." - Illinois state Transportation Secretary Kirk Brown, commenting on the "Heart of Illinois" Peoria to I-180 proposal. I-74 and I-55 lead motorists to Chicago on a route about 7 miles longer than the proposed new freeway.
I-180 (numbered as another interstate) California
An interim number (1978-1983) for the Richmond-San Rafael stretch of what is now I-580. Before its promotion to interstate status, this route was part of CA 17. California already has an established state route 180 passing through Fresno, making the I-180 number unavailable. 
13.19 miles ; south from I-80 near Princeton to Hennepin (2000 population: 707).
A Necessary Interstate?
Interstate 180 has earned some notoriety as a front-runner for the nation's least necessary interstate spur. At its end is a town with the population of a wedding banquet, and a steel mill that has changed hands a few times as companies go under or merge (LTV, ISG, etc.) Today, the highway is very lightly traveled.
However, couldn't I-180's condition be blamed on the decline of American steel in general? Certainly when it was built, there was a critical need for it?
Sorry; that's not the case. Let's rewind to the 1960s, when it was planned and built.
I-180 was added to the Interstate system on Jan. 25, 1967;  and opened in the fall of 1969. . In 1970, a study by the General Accounting Office (GAO) concluded that I-180 was constructed to satisfy the demands of a steel company (Jones & Laughlin) looking to locate a plant in Hennepin. By objective criteria, more important routes in Tacoma and Tucson were turned down at the same time I-180 was approved. 
"No other interstate route has been constructed primary to serve a private manufacturing company, and no other interstate spur serves an area with such a small population," the GAO said. .
Another surprise: the $44M freeway's cost per mile was about four times the prevailing rate at the time. 
The Heart of Illinois freeway proposal
The state's mid-1950s interstate highway plan included a freeway from Peoria toward Chicago in the I-180 corridor. This was not approved by the FHWA, but the state made provisions for the highway in Peoria ("ghost ramps" from IL 6 at the IL 29 interchange, and an I-180 stub at its IL 29 interchange).
In the mid-1990s, the state revived the proposal, calling it the "Heart of Illinois Freeway." A few alternatives were selected, among them the IL 6 to I-180 connection.  In late 2000, the state decided to proceed with the 6/180 connection, but ran into opposition from farmers and withdrawn support from area state senator Ray LaHood (R, Peoria), who favored four-laning IL 29. 
A Peoria city council vote to encourage IDOT to continue study on the freeway failed, highlighting the proposal's loss of momentum.  In February 2002, IDOT stated there was no traffic need for the freeway, only political and economic reasons for advocating it; and that they only studied the issue because Peoria asked for it. 
Part of late-1960s Supplemental Freeway Plan
In the 1960s, Illinois adopted a freeway plan with the goal of providing any state resident a trip of 30 minutes or less to reach a "convenient highway" reaching any city of 25,000 or more.  The I-180 to Peoria extension was part of this plan, but few of these freeways were actually built (I-39 is one that was). 
Hollywood, here's your freeway set
Brian DeSalle writes that in the summer of 1999, when he worked as an intern for IDOT, sometimes 30 minutes would elapse on I-180 without a single car passing by. The highway had just completed a major resurfacing project, including some portions that had not been repaved since it opened. 
"I-180 is the poster child for the modern Interstate highway after it was redone last year. It has wide lanes, very wide shoulders on each side, the bridge decks are new, the ramps are long, and everything is very well signed." - John A. Weeks III, in 2003 
28.85 miles ; from I-80 into Williamsport. Before 1985, was part of PA 147. Going even further back, in 1934 PA 147 was part of US 111.
See also: I-180 History (Jeff (Kitsko)
I-180 (numbered as another interstate) Pennsylvania
1.09 miles . Wyoming's only 3di is in Cheyenne. It's not even a freeway; instead, it's a four-lane divided road with two at-grade traffic-lighted intersections. Even the interchange with I-80 is only a diamond. Under construction for about six years, it completely opened, with ceremony, on June 1, 1984.
Why is a non-freeway given interstate status? Wyoming's original request was for a freeway spur to downtown Cheyenne. However, for reasons of access (getting to the freeway viaduct would be difficult from the south side of Cheyenne, between the UP railroad tracks and I-80) and cost, the state pressed for an expressway instead, and got a loophole for interstate funding. 
See also: I-180 (Andy Field)