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4.42 miles ; Interstate 195 is the Julia Tuttle Causeway, leading from I-95 in Miami to FL 907 in Miami Beach. It opened on Dec. 23, 1961. Had funding been available at the time, the FL 112 continuation westward could have been designated I-195 as well. However, Florida built FL 112 on its own as a toll road, which at the time was ineligible for interstate designation. 
4.71 miles ; from I-95 in Hawthorne (Baltimore suburb) to Balto-Wash. International Airport (BWI).
The first part of what is now I-195 opened as MD 46, a spur from the Baltimore - Washington Parkway to BWI. In 1971, I-95 opened in the area, along with a short expressway to US 1. Mike Pruett writes that the I-195 designation might have been cancelled and then revived, based on Rand McNally maps: in the 1970s, they showed I-195, but in the '80s displayed MD 166 and MD 46, before returning to I-195 in 1990. The Federal route logs for 1971 and 1978 show I-195 added somewhere between those two years.  
In June 1990, the final segment of I-195 between the B-W Parkway and US 1 opened, completing the gap. MD 166 now ends at the I-95/I-195 interchange, and MD 46 no longer exists. 
I-195 Massachusetts; Rhode Island
44.55 miles ; from Providence, R. I. to I-495/MA 25 in Wareham, Mass. The Rhode Island section opened in 1962; the Massachusetts part was finished in 1970. The section from South Providence to Fox Point, the earliest of Providence's interstates, opened in 1956. 
Speed limit setting dates might be opening dates
John F. Carr sent information from state speed limit regulations that might show exact opening dates of I-195 in Massachusetts: 
Relocation in Providence
Rhode Island plans to straighten and shorten 2.5 miles of the highway near downtown Providence, building on a new alignment 0.5 mile south of where it is now. Why a new route? The current route (dating from the 1950s) has winding curves and several bridges near end of life; the new alignment will get a safer bridge and new interchange with I-95, without interfering as much with traffic on the current alignment.
The city will also benefit from some valuable land made available, and some neighborhoods no longer cut off from the city. "By moving the highway you can undo some of the mistakes that engineers made in the '50s," said Dan Baudouin, executive director of the Providence Foundation. Work will cost about $250 million and last about six years. 
In Fall River, Mass., the Government Center building was built over I-195 in 1976: reportedly the first public building over a federal highway. 
I-195 (proposed number rejected) North Carolina
This was a 35-mile new route submitted by the state to AASHTO in 2003. Interstate 195 would be defined "[b]eginning at the intersection of Interstate Route 95 and a new facility being constructed north of Fayetteville, then northwesterly, southwesterly, southerly and southeasterly over the facility for 35.18 miles to the intersection of Interstate Route 95 south of Fayetteville." 
This was the Fayetteville Outer Loop, with both ends at I-95. The selection of a spur number ("195" starts with an odd digit) was surprising. AASHTO rejected the numbering proposal on May 30, 2003, saying the FHWA had not designated the route as a part or future part of the Interstate system. 
In early 2004, NCDOT published a planning map showing I-295 for the loop. That number will eventually be resubmitted to AASHTO.
I-195 New Jersey
Parts of this highway were open in 1974. Corridor hearings for the eastern section, from CR 527 to NJ 34, were held in 1969. An environmental impact statement (EIS) was completed in fall 1971 and approved by the FHWA in November 1971. Design work started, and the design public hearing was held in March 1973, with initial design phases approved in 1974.
By 1975, however, new air quality regulations were issued, and right-of-way for I-195 could not be acquired until a new EIS was generated. 
However, construction eventually started, and the whole thing was complete by 1989.
"IIRC, I-195 was sort of a "consolation prize" for not getting I-95 completed." - Adam Froehlig 
Extension to Pennsylvania planned
Big changes are in the works for I-95, I-195, and I-295 in the Trenton, N.J. region. In 2012, a direct interchange between I-95 and I-276 in Bristol, Pa. is planned to open (currently, there is no direct connection at all). Pennsylvania and New Jersey have agreed on numbering changes to take place at that time (though AASHTO has not yet signed off on them): 
3.24 miles ; mostly 6 lanes; from I-95 and I-64 to VA 195 (Downtown Expressway) in Richmond. The 3-mile section from I-95/I-64 to Powhite Parkway opened in 2 sections on July 15 and 19, 1975, and the 0.5-mile connector to the Downtown Expressway opened on February 3, 1976.  Though maps are have been vague on this short route, it has officially had interstate designation throughout .
The freeway was planned in the 1960s as the Beltline Expressway, part of a planned 10-mile toll system including the Powhite Parkway and Downtown Expressway. Because rising costs were helping delay construction of the highways (a nasty inflationary positive feedback loop), city and state agencies had already tried, and failed, to transfer some mileage and funding from the proposed Interstate 295 beltway to the Beltline Expressway. 
In 1968, Congress authorized an additional 1,500 miles to the Interstate Highway System. Dozens of states' requests for new routes included Richmond's Beltline Expressway. On July 18, 1969, 90% funding for 3.3 miles was approved, enabling the highway to be constructed as Interstate 195, a toll-free road. The Powhite and Downtown were built as toll roads.  
The highway follows the James River Branch (Beltline) of the Richmond, Fredericksburg and Potomac Railroad, an alignment laid out in 1888. 
The 1978 US DOT Route Log had 9.2 miles assigned to I-195 .