If you ever drive I-80/I-90/OH Turnpike between the I-75 and US-20 exits, the highway crosses the Maumee River. Just to the north side of the bridge, running almost parallel, is an abandoned railroad trestle. This bridge belonged to the Toledo Terminal, a switching railroad that made a complete loop around the city, and is a swing bridge that was never used. Supposedly, it was because the expected heavy industry on the upper Maumee never materialized. The bridge last saw use in 1982 when it was damaged by a train derailment, and is now proposed for demolition.
(Edit: Demolition has since begun, and is about halfway razed as of New Years)
The downstream counterpart to this bridge is also movable and is still in use.
In a completely different location, a rail bridge over the Delaware and Raritan Canal in Princeton, NJ (used by the "dinky") is a swing bridge. It probably hasn't moved since the 1930s, or whenever the canal was retired from service.