When I started riding my bicycle to work in February 2008, I got by with what I had, namely a Nishiki Olympic 12 that I had bought new in 1984 and used for commuting in Los Angeles during the mid-80s. I hadn't ridden it much the previous 20 years so it was still in good shape. The only thing I did to it was add a trunk bag to the rear rack. It got me where I wanted to go.
On my second bicycle commuting attempt, I went down and bent the frame on the Nishiki. Although it was still roadworthy I was on the prowl for a new bike. In August 2008 I got a good deal on a hybrid. As it turns out, it was another Nishiki, this time a Sport XRS. This turned out to be a better bike for commuting, and with some extra modifications it is even more well-suited to the job.
The bicycle itself is better for commuting. As a hybrid, it has wider tires, upright handlebars, and low gears (21 of them). Also, being 10 years newer than the Olympic 12, the Sport XRS has some nice modern touches including cantilever brakes and indexed shifters. No more hunting for the right gear; a quick twist of the wrist, a click, and I'm there. Added together, all these features make this bike is far more nimble and visible in traffic. This really is a good "city bike."
I didn't stop there, though. If you look you'll see other differences compared to my Olympic 12. The Sport XRS has full Planet Bike Freddy Fenders, panniers on the rear rack (one of which holds much more than a trunk bag), and four lights, two in front and two in back. Between dusk and dawn I leave one headlight and one tail light on constantly, and put the other one at each end in flash mode. During daylight hours I just put one light on in front and in back, both in flash mode.
I added a bell on the handlebars to help communication with pedestrians and other cyclists. Although the bike came with a flat bar (mountain-bike style), I made it a little more comfortable by adding an Origin8 Space Bar which is more comfy on my wrists.
So to sum up... I started out simply. You can too. Any old bike can be converted into a commuter. But if you are buying a bike for commuting, consider your ride. If you'll be facing traffic, consider an upright bike. If you have a longer commute (mine is about 15 miles round trip), a road bike might be better. Either way, take into account that once you start commuting, you'll want to add to your bike to tailor it to the job, adding storage, lighting, etc.