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The Pasadena Freeway (CA 110), originally the Arroyo Seco Freeway, opened in 1940 as the first freeway in California.
"You know how it's done
-- Ice Cube, "Down for Whatever"
20.43 miles ; Harbor Freeway, from I-10 south to CA 47 near Long Beach. The Pasadena Freeway continues north of I-10 as CA 110 (see sidebar).
The first section of the Harbor freeway opened in 1952; the last, in 1970.  Originally it was signed as part of US 6 and CA 11; in 1964 US 6 was truncated to US 395 in Bishop.
In 1996, the $498 million Harbor Freeway Transitway opened; 10.3 miles of bus and carpool lanes in the I-110 median. There's room for light rail as well. A way cool 2.6 mile-long viaduct on Y-shaped columns rises up to 50 feet above the roadway, and above surface streets which overpass the regular 110 lanes. These lanes have separate ramps to the Interstate 105 HOV lanes. Planning began in 1979; construction began in 1989. 
I-110 (preliminary numbering) California
On April 1, 1958, California submitted to AASHO a numbering plan for its proposed interstates, including 3-digit spurs numbered in the low 100s and not associated with their parent interstates. Interstate 110 was the proposed number for, of all things, I-480 in San Francisco. 
This number was not compliant with AASHO's numbering convention and was rejected.
On August 7, 1958, California had bought in to the system and submitted I-480. This was approved, along with the rest of California's original interstate highway system, on Nov. 10, 1958. 
I-110 (decommissioned) California
An old 1960s numbering for a short section of the San Bernardino Freeway between I-5 and US 101 in Los Angeles. (This is the top of the narrow triangle I-5, I-10, and US 101 form.) 
It's not certain whether this was ever signed; the answer is probably "no." There are no interchanges between the termini of this section.
6.94 miles ; south from I-10 in Pensacola. Date of birth is unknown; appears to have existed as early as 1965.
Extension proposed in 2000, dropped
There were plans to extend Interstate 110 north of I-10: at first, less than 2 miles, to Nine Mile Road, for local traffic relief; and in the future, possibly to I-65 in Alabama.  The immediate roadblock was a lack of secured funding.
The Escambia County Expressway Authority, formed in 2000 to decide whether building a 1.8-mile extension was feasible, determined that toll revenues would cover only about 30% of the $50 million needed to finance its construction. In mid-2001, the group was to decide whether to cancel the project or hand it over to the state. On May 31, it decided to solicit interest from the Florida Turnpike authority; if rebuffed, the group would return to a cancel vs. state funding vote.  
Both extension ideas were later cancelled. 
8.89 miles ; runs north from I-10 in Baton Rouge.
Plans for the Greater Baton Rouge Expressway, designed to connect I-10 and downtown to industry in the north, were unveiled in the late 1950s. Construction began in 1961, and I-110 was finished in 1984. 
Some early 1960s design features on the highway, such as left exits, are now obsolete, but reconstruction would be quite expensive. 
4.096 miles ; runs south from I-10 in Biloxi. Complete from I-10 to Bayview Dr (south end of the Back Bay Bridge) by 1981. The southern mile (all elevated) from Bayview Dr to US 90 was not complete until 1988. 
I-110 (not signed as interstate) Texas
0.92 miles ; south from I-10 to the Rio Grande in El Paso. Interstate 110 is not well-publicized in Texas, even though it appears on route logs and some maps; to the motorist, it's signed US 54. Before the US 54 freeway was extended north of I-10, however, I-110 signs were posted on the portion to the south.