Chicago's bridge history includes five types of movable bridges - floating, swing, vertical lift, rolling lift bascule, and fixed trunnion bascule. Bridges within the Loop are all fixed trunnion bascules. Taking a trip south of the Loop to Chinatown, you can find the rolling lift bascule and a vertical lift bridge. If you take a short trip north you can take a good look at swing bridge.
A short ride north on the CTA's Red Line from the Loop can give you an interesting contrast between the old and the new in Chicago's bridges. Get off at the North / Clyborn stop (CTA Trip Planner). Walk west about 0.4 mile on North Avenue to the North Branch of the Chicago River.
The bridge carrying North Avenue across the river is a 2008 bridge. The steel truss bridge crossing to the south to Goose Island, is a 1902 bob-tail swing bridge.
This bob-tail swing bridge at Cherry Avenue connected North Ave. to Goose Island. This bridge was restored in 2009. While the bridge is no longer operable, it is easy to view, up close, the key components of the bridge (like the turn-table shown in the photo below). More information can be found at Historicbridges.org. A photo of the plaque is also shown on this page.
The current bridge at North Avenue opened in 2008. It is a fixed, hybrid cable-stayed / suspension bridge (see photo). It replaced a first generation Chicago-Type bascule. While neither the Cherry Avenue nor the North Avenue bridges are moveable, this location brackets 106 years of Chicago bridge history in one location. You can read more on the the current North Avenue bridge here. For information on the bascule, see Historicbridges.org.