The truth is that given Chicago's topography, there are at least a half dozen attributes other than weight that should matter to roadies and commuters alike. Still, a responsibly light bicycle can be safer, more comfortable, and just simply sexier than your average ride. So given our lack of meaningful elevation, my feeling is that weight reduction should not be made at the expense of durability or ride quality -- tradeoffs worth considering if you're living in, say, Colorado. So here's a simple guide for weight reduction on a few different form factors.
70s/80s Roadie/Commuter, French/British/American
Your vintage Peugeot/Raleigh/Schwinn probably has its fair share of steel bits and comes in over 26 pounds. You probably didn't pay too much for it, but it's damn cute and isn't too much of a theft target. The biggest improvement you can make is replacing the wheels. If you're lucky, you'll have long reach brakes that will allow you to swap the 27" for 700c -- so pick up a pair of used road wheels and slap on some nice tires and you'll transform the ride while dropping a pound or more. Other easy targets: steel seatposts, steel railed saddles, pedals.
70s/80s Roadie/Commuter, Japanese/Italian
Nicer examples are already plenty light, in the 23 pound range. Assuming the wheels are decent, these Olmo/Bridgestone/Colanago/Miyatas can benefit from weight reduction tied to aesthetics. Dump the 400g saddle for a modern 250g model and replace the handlebar tape to match. If the bike is Campagnolo-equipped, forget swapping components -- but if it has Japanese components, take a look at the handlebars, as these were occasionally steel. A set of new tires won't necessarily reduce weight, but they'll likely improve the ride. If your bike has steel skewers, replacing them with the alloy allen-key style can drop 150g.
Crappy Fixie
Oh, where to start? If this is a modern example (Bianchi/Fuji/KHS/clone), there's not much you can do, as the entire build is just mediocre. One interesting strategy is to replace the stock (steel) fork for a carbon model, shaving over 200g and smoothing out the front end handling. For vintage or DIY conversions, dump the wheels/tires and steel seatposts, saddles, pedals. It's pretty easy to get fixies under 19 pounds.
Modern Roadie, Off the Shelf
Big brand road bikes have come with decent generic aluminum stems, bars, seatposts, and saddles for a decade or more -- so if you don't mind the fit or finish of these bits, ignore them. (Carbon won't drop meaningful weight in these areas.) But many of these bikes have really crummy cranks (often triples!) -- so moving to one of the new external bottom bracket/crank combinations can easily drop 2-300g while improving stiffness and power transfer.