A few swing bridges still exist, with likely the best-known one on the north branch of the Chicago River at North Avenue. It is still in use, though minimal. In 2007 it was granted historic landmark status.
The longest surviving swing bridge is at Kedzie near 35th St, at a whopping 479.5ft. It was constructed in 1899, largely due to the Chicago River's flow reversal efforts. Although it is in use, the bridge has allegedly not been opened since 1953.
Here is a photo of the Lake St bridge, back in 1875, swung open to allow passage of river traffic.