What Kind of Bike should I ride?
There are a lot of different kinds of bikes out there. Here are the basics. I've only included viable commuter bikes and ommitted those that don't make a lot of sense such as BMX, and beach cuisers.
Road bikes are what you might call a "ten-speed" if you haven't been on a bike in a while (most of them are 21 speed these days). They have very narrow tires and dropped handlebars (think ram horns). These are very efficient bikes, light and fast. Road bikes are less able to deal with pot holes and cracks in the pavement than other types, and they can be somewhat uncomfortable for casual riders, as they put you in a hunched-over position. I'd suggest a road bike if you have a good quality paved trail or bike lane, and you want the maximum amount of your pedaling effort to go into moving the bike forward. Also, on long commutes (10 miles or more), you might find a little relief in the three different posible hand positions on those drop bars. Road bikes do not have suspension (shock absorbers).
Road bikes are popular commuters, and I ride one myself. You get used to the minor discomforts pretty quickly, and the pedaling efficiency can't be beat.
A variation of the road bike is a Cyclocross bike (often just called a "cross bike"). These are basically road bikes with hardcore brakes and somewhat-knobby tires. These are a great option for commuting!
Mountain bikes are very popular for the casual commuter. The big, soft tires and shock absorbers soak up some of your pedaling energy along with the bumps, and mountain bikes are often heaver than road bikes - so they are not quite as efficient to pedal. Many new riders, however, find the flat-style handlebars more inviting, and the mountain bike is certainly better able to deal with ruts and pot holes. I'd suggest a mountain bike if your commute is 5 miles or less, and especially if you have gravel or rough pavement to deal with. Most mountain bikes have front or full suspension. They are designed and built for off-road riding, and they are at their best in the woods, but people love them, even in the city.
Hybrid Bikes (AKA City Bikes)
Hybrids are supposedly the best of both road and mountain bikes, made for city riding. They offer the comfort and familiarity of a mountain bike, with narrower, smooth tires for city riding - although the tires are notably wider than those of road bikes. This is a popular style, feels like riding a mountain bike, but more efficient. Hybrid/City bikes are perfect for commutes on paved roads or urban trails, even if the road is a little rough. They are not quite as efficient as a road bike, but much more comfortable for a lot of people, especially if you are already familiar with mountain bikes. most hybrid bikes do not have suspension (shocks), although some may sport front shocks. Giant is calling their electric bikes "hybrids". Most of the rest of the world, however would call those "electric bikes" and use "hybrid" to refer to the mountain/road bike crossbreeds described here.
Comfort bikes are made for Sunday Cruises along the waterfront. They place the rider in a very upright position, which is indeed more comfortable, but not maximized for speed or efficiency. If you have a bad back, or you want to smell the roses on your way to work - look into comfort bikes. I don't think I'd suggest one for rides longer than about 5 miles, but I don't really know, I've never ridden one. They look heavy, and that means more work to pedal. I could be wrong. Go test ride one! Most comfort bikes have a large soft seat, front suspension and quite often seat-post suspension too, to absorb the bumps.
Electric bikes have really come of age, and you see more and more of them around every day. They are really one of the smartest options if you are just looking for easy and affordable trasportation. Most electric bikes are variations of a hybrid or comfort bike design. They can achieve ranges averaging around 30 miles per charge, and can get you to work without sweat or spandex. More info here.
Folding / Small-Wheel Bikes
Folding bikes are great for train and bus commuters, or people who don't have a good parking option at the office. Folding bikes collapse small enough to stash under your desk or in a closet at work. I have never commuted on one for more than a mile or two, so can't give a full review. Maybe I'll get one just to give a better review. Small-wheel bikes and folding bikes often look alike, since most folders have small wheels, but not all small-wheel bikes fold. Small-wheel bikes are surprisingly ridable and fast - and feel quite like a "normal" bike. Invented by Alex Moulton and made popular by Bike Friday and Brompton.
Where to get a bike
You can get a bike from a bike shop, a department store, or used from an individual. If you don't know what to look for, I'd suggest a bike shop. They don't stock crappy bikes and they can be very helpful in getting you on the road with all the tips and gear you need. Most people at bike shops ride a lot themselves, that's why they work there - it's not for the pay! They love bikes and they know them inside an out.
Department stores on the other hand (Target, Fred Meyer, Etc.) ONLY stock crappy bikes, and their employees know exactly squat about them. Don't waste your time there, even if you don't want a fancy-pants race bike. Department stores still suck. Tell the guy or girl at the bike shop what you want, they have humble daily-driver bikes too - they are just GOOD humble daily-driver bikes.
If you know what you want, I'd suggest Craigslist or the local classifieds to get a great deal. Another benefit of the bike shop is the after-sale support, repair shop, etc. Most places will give you a free tune up if you buy a bike there. Happy hunting!