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60.64 miles ; from I-75 down through Tampa and St. Petersburg, over the Sunshine Skyway (cable-stayed bridge across Tampa Bay) to reunite with I-75. I-4 ends at I-275 in Tampa, the only place (trivia fans) where a 1di ends at a 3di.
Originally (1958), I-75 was to end at I-4 in Tampa, and then I-4 alone would continue into St. Petersburg, and end near the beaches. Florida had pushed for an extension of I-75 to Miami, but all miles in the interstate system were already allocated. 
In 1968, Congress approved 1,500 additional miles, and the Miami extension was alive. I-75 was extended over I-4 through St. Petersburg and the Sunshine Skyway on May 14, 1971. 
Meanwhile, the state was planning an interstate bypass of Tampa Bay to the east, to be called I-75E. AASHTO was discouraging letter-suffixed interstates by this time, and on August 24, 1973 the bypass became I-275. 
In 1972, a traffic study showed that the freeway through Tampa and St. Pete would be inadequate for the traffic a principal interstate highway would carry. Officials considered directing thru traffic along the bypass with special guide signs, but decided that designating I-75 along the desired through route would be more effective. In 1980, I-75 and I-275 were swapped, and I-275 was located where it is today. 
The construction of I-275 reportedly ripped up many urban neighborhoods, and displaced ten black churches. 
About the Skyway
The original dual-span bridge, built in 1954, was struck at the southbound span by the ship "Summit Venture" on May 9, 1980. The main span collapsed and 35 people perished.
Emergency relief funds helped the Florida DOT build a $240-million replacement cable-stayed bridge, which opened on April 30, 1987. The New York Times said the new bridge "may rank as the most impressive pieces of large-scale bridge design in this country in half a century." 
The undamaged northbound span of the old bridge was demolished in 1994. Some unattached portions were left standing and converted into fishing piers; one of them, at 1.6 miles, is the longest such pier in the world. 
For network geeks...
The Sunshine Skyway graces the cover of The DHCP Handbook, by Ralph Droms and Ted Lemons.
29.97 miles ; from I-75 south of Flat Rock to I-96, I-696, and M-5 in Farmington Hills and Novi. Western bypass of Detroit. Built between 1974 and 1977. In 1958, Michigan wanted to call this highway Interstate 73, and call the Saginaw loop (today's I-675) Interstate 275. 
Was intended to reconnect to I-75
Original plans included extending Interstate 275 northward through Oakland County to meet I-75 north of Clarkston.  This was cancelled with the help of local opposition, but increased traffic in the area is leading to calls for better north-south facilities in the area -- from building arterials to reviving the 275 proposal. An MDOT official has stated that they "haven't driven the final nail in the coffin yet." 
Led Zeppelin's "Trampled Underfoot"
In 1997 Chris Bessert (MichiganHighways.org) wrote:
[I-275] is literally falling apart. If it weren't for the asphalt patch the MDOT keeps throwing into the craters, we'd have ourselves a GRAVEL freeway, that's how bad it's getting. Supposedly, the MDOT tried what they called a "new innovation in concrete" back in the 70s. Well, that didn't seem to work out as well as hoped. We're "celebrating" twenty years of I-275 and it's junk." 
The next two years, I-275 was rehabilitated. The portion between M-14 and I-94 was redone in 1998, and the portion between M-14 and I-696 in 1999. 
I must add that among the vehicles pounding the concrete on I-275 are the coolest trucks in America: 42-wheel, 11-axle monsters that are only allowed in Michigan. Some steel hauling trucks have eight axles in the trailer, leading to the term "centipede."
I-275 Ohio; Indiana; Kentucky
83.71 miles ; full beltway around Cincinnati. This Interstate 275 is the only 3-digit interstate to go into 3 states. It doesn't spend much time in Indiana, but does have one interchange there (US 50, Lawrenceburg).  The first section to open was between OH 4 and I-71 in the early 1960s. The whole route was completed in 1979.
I-275 doesn't work well as a bypass
Although I-275 is a complete loop around the city, it apparently wanders too far afield to be a convenient bypass route. David Sturm writes: "The [downtown I-75 traffic] problem always radiates back to 275 being absolutely the worst 'bypass route' imaginable for I-75. It's no wonder the corridor is so burdened by traffic.... No one I know regularly seeks to bypass Cincy on 275. It would have been better numbered 271 or 274." 
Jack Mecklenborg elaborates: "23 miles of I-75 bisect the I-275 loop almost perfectly, with 46 miles to the east and 43 miles to the west. Therefore I-275 is not of much use as a bypass and relieves a negligible amount of through traffic from I-71, I-74, or I-75... it is reasonable to assume that had only the sections near the radial expressways been built that an incomplete I-275 would have attracted a similar number of vehicles to today's complete loop." 
At first look, the I-275 designation seems unnecessary, since I-75 could continue straight to I-40 in Knoxville instead of bypassing the city. Originally, I-75 did that, meeting I-40 at the notorious "Malfunction Junction" interchange.
In the late 1970s, work began on I-640, a bypass route intended to relieve traffic through downtown. When this opened in April 1982, I-75 was rerouted onto I-640 leading southwest, and the portion of former I-75 was designated I-275.