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3.30 miles ; this is the official length, but drivers will only see about 1 mile on this short connector from I-280 to US 101/San Francisco International Airport in Millbrae. Its single interchange between the two termini is with El Camino Real.
The state has proposed extending I-380 westward to CA 1, and the 280 interchange shows room for this; and this might account for the extra 2 miles in the official length.
A 1960 San Mateo County plan proposed a state freeway in the I-380 corridor, extending from CA 1 east to a proposed Bayfront Freeway (CA 87), east of US 101, that would either be built on fill, run on an aqueduct, or simply be underwater.
In 1964, the proposed route was given a number: 186. On December 24, 1968, it was given Interstate status from I-280 to the San Francisco airport. 
I-380 is called the Portola Freeway, named after California's first Spanish governor, Gaspar de Portola. He was the first European to discover San Francisco Bay. Named by Assembly Concurrent Resolution 113, Chapt. 217 in 1970. [Caltrans]
See also: I-380 (Dan Faigin)
73.05 miles; from I-80 outside Iowa City to Waterloo. There, a US 20 freeway is slowly growing its way across the Hawkeye State. The first segment opened Dec. 19, 1973; the final segment opened Sept. 12, 1985. 
I-380 was originally planned to extend to Cedar Falls (in fact, the 1978 Federal Route Log lists I-380 as 79.56 miles), but in 1982 the city of Waterloo traded those funds in for other projects (per the Interstate Substitution ("trade-in") rules established in 1973). Part of the proposed I-380 freeway north of downtown Waterloo opened in 1992, but it is signed as US 218. 
Jason Hancock writes:
"Although there are "I-380 ENDS -- 1/2 MILE" signs north of the San Marman Drive exit in Waterloo, the exact end of I-380 (which, according to IaDOT publications, is the signaled intersection with Mitchell Avenue) is not marked. Similarly, the only sign of the beginning of I-380 (southbound) is an overhead sign for Exit #72, with an 'Eisenhower Interstate System' sign on the pole -- there are no I-380 signs until the interchange with US 20."
I-380 (numbered as another interstate) Iowa
In preliminary plans, I-235 through Des Moines would have also been signed I-380. On Nov. 10, 1958, AASHO approved Iowa's interstate system, but specified that the superfluous I-380 designation be removed. 
See also: Interstate system route numbering (Stephen Summers; FHWA and AASHTO info)
24.76 miles ; from I-84/I-81 in Scranton (Dunmore, actually) southeast to I-80 near the Pocono International Raceway. Formerly I-81E until about 1973; in 1968 there was no freeway and you took US 611 instead. Completed in the late 1970s.
I-380 (numbered as another interstate) Pennsylvania
In 1958, according to a New York Times article*, Interstate 380 was to be the numbering for: 
* "New Roads with New Numbers Will Parallel Old U.S. Routes". New York Times, September 19, 1958. I haven't seen the article yet.