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I-595 Florida (link)
12.86 miles ; the Port Everglades Expressway, from I-75 at FL 869 to US 1 in Fort Lauderdale.
Before I-75 was extended from the Tampa area to the Miami area, the two-lane FL 84 (aka "Alligator Alley") crossed the Everglades from Naples toward Fort Lauderdale. By 1969, a four- to six-lane Port Expressway was planned to connect Alligator Alley to US 1. This was planned to be a toll road. 
Eventually I-75 was routed along Alligator Alley, but then would turn south toward Miami. The Port Expressway would then connect two interstate highways, and was given an interstate designation itself: Interstate 595.
A 2.3 mile section near FL 869 opened in May 1988; the 5.3-mile link east to the airport opened on Feb, 23, 1989.  
I-595 (cancelled) Maryland (link)
This proposed spur into Baltimore, in existence for only a year, would have incorporated part of previously cancelled I-70 and I-170. (There is another I-595 in Maryland, a secret designation of US 50/301; see below).
Please see Scott Kozel's Baltimore Interstate System Map, which will provide essential context. As the 1980s began, the plan to extend I-70 to I-95 was in trouble. In 1981, a portion of I-70 leading west from proposed I-170 was cancelled, leaving I-170 and the remaining portion of I-70 disconnected from existing I-70.
This leftover portion, a 2.9-mile stretch, was designated I-595 in 1982.  It incorporated 0.9 miles of unbuilt I-70, 0.7 miles of unbuilt I-170, and 1.3 miles of I-170 that opened in 1979. However, I-595 was cancelled in July 1983; other transportation needs in Baltimore were so great that even its 10% share of interstate work was judged to be better spent on other projects. 
A few years later, Maryland revived the I-595 designation as an unposted third route number for the D. C. to Annapolis segment of US 50/301 (see below).
I-595 (not signed as interstate) Maryland (link)
19.97 miles ; a "secret" designation along US 50/301 from I-495 near Washington, D. C. to MD 70 near Annapolis, Md. It's not signed Interstate 595 because the existing 50/301 designation is more familiar and (among a thicket of x95 interstates in the region) less confusing. When interstate-funded improvements were completed in 1995, Hal Kassoff, head of the Maryland State Highway Administration, declined the public I-595 numbering. 
Apparently the only proponents of adding I-595 shields would be fellow roadgeeks. In 2001, in a letter to historian Scott Kozel, the Maryland DOT stated that adding the 595 numbering to US 50/301 "would [not] serve any useful purpose for the traveling public."  In early 2002, Washington Post commuter columnist "Dr. Gridlock" remarked, "So hats off to Hal Kassoff. We don't need more derivations of I-95." 
...was an early I-68
Scott Kozel writes:
"The U. S. 50 expressway from D. C. to Annapolis was opened around 1957. It had two lanes each direction. Around 1980, the need became apparent for widening and interchange improvements. Interstate money became available when several planned interstate segments were deleted in Baltimore, about the mid-1980's. The segment of Rte. 50 from I-495 to Annapolis was approved for interstate construction as I-68.
In anticipation of the National Freeway opening, AASHTO approved moving the I-68 designation and reusing the I-595 designation on June 6, 1989. 
A December 1988 listing of road work published in an Annapolis newspaper showed the I-68 designation extending to the bridge over the Severn River, and only US 50/301 continuing east. 
Was it always intended to be secret?
Mike Ballard reports that some freeway signs in the I-495/US 50 east area have empty spots which were probably set aside for I-595 shields. Also, Phil Delaney recalls seeing I-595 shields there around 1991. 
See also: I-595 in Maryland (Scott Kozel)
I-595 (cancelled) Virginia (link)
This was to be US 1 (Jefferson Davis Highway) south of I-395 to VA 233, widened to 8 lanes and elevated; about 1.1 miles. . In the face of local opposition the design was downgraded to six lanes with access partially controlled.
You can see vestigial I-595 ramps at the US 1/I-395 interchange; these were built when I-395 was reconstructed in 1975. A contract was awarded that year to construct the rest of the freeway, but a court injunction several months later halted construction. The road was never signed as I-595. 
US 1 was ultimately built with Interstate trade-in funds as a signaled, but raised roadway through Crystal City, and running due east into National Airport just south of Crystal City. 
See also: Washington, D. C. Interstates and Freeways (Scott Kozel)