Pennsylvania
New Jersey/New York
None of I-78's spurs actually intersect it. In fact, it ends at the foot of the Holland Tunnel in Manhattan.
I-78 follows a pair of one-way streets in Jersey City, NJ. This is only the second instance where an Interstate is actually routed onto surface streets (I-70 in Breezewood, PA is the other).
I-278 goes through all of New York's five boroughs, connecting to Manhattan via the Triborough Bridge.
I-478 is the route number for the Brooklyn-Battery Tunnel, which carries motorists to and from Lower Manhattan.
I-678 is a spur from the Bronx to Queens that ends at the John F. Kennedy International Airport.
I-878 is the shortest unsigned Interstate. It is signed as NY 878, the route number for the Nassau Expressway, a crazy one-way corridor leading from the Belt Parkway to the JFK Airport.