Interesting thread. The Caprice is actually back around, but only offered as police/detective cars as far as I know, but still can be sold to the public I think?
Not sure about longest, many of those that have been mentioned, but some long running names that come to mind are...
Chevy Impala has been around since 1958 - still going, though the name was not used from 1986-1993. Camaro around since 1967. Chevy Malibu around since 1964 (though name was not used from 1984-1996).
Buick Century name was used the mid 1950s up through the 2000s (re-introduced in 1973 after being not used in the 1960s). By 1982, it was a small FWD car (by 1980s standards).
Pontiac Bonneville around from 1958 until 2007-08 I believe.
Chevy Silverado name since 1973.
Some long running import names that have went on... Honda Civic (since 1974), Honda Accord (since 1976), Toyota Camry (since 1983), Toyota Corolla (since 1967 I think?), Nissan Maxima (since 1980-81).
A lot of makes will redesign and change the names of the redesigns, but I guess a lot of these best sellers like Accord, Camry, F-Series trucks, Silverado, you just don't mess with the names.