Will I ride my bicycle on paved roads, or on trails or fire roads?
If you plan on doing serious off-road riding, you need a serious off-road bicycle. Get a mountain bike! There's a wide variety of mountain bikes available with or without front and/or rear suspension but that's a discussion that will have to wait for another day. Only with a decent mountain bike will you be able to competently maneuver your bike along single-track, down a mountainside, or over rocks.
On the other hand, if you are going to stay on well paved streets, you probably don't want to be slowed down by the weight and rolling resistance of a mountain bike and should look for something else.
Do I want to ride distances greater than ten miles?
If your going to ride more than about ten miles on the road, stay away from mountain bikes. While I've gotten a lot of good city riding with my mountain bike (equipped with 1-1/4" slick- treaded, high-pressure tires), I wouldn't want to be on it for more than about 30 minutes at a time on the road. Sure it's great off-road, but you'd be more comfortable and faster on a bike built for the road.
Do I want to carry my own equipment while touring?
If the answer is yes, try to get a touring bike. Although fewer manufacturers are making touring bikes these days, they can still be found if you're willing to look. Bikes built for loaded touring are usually more comfortable than other bikes, are more stable (they turn more slowly), and also come with eyelets in the frame and fork for attaching racks. Touring bikes also come with a triple crank to accommodate smaller gears. Sure, mountain bikes and some hybrids also have eyelets and triple cranks, but they are not conducive to riding great distances. And, after all, who wants to be uncomfortable on a long touring ride?
Would I rather sit in a comfy chair or on a skinny bicycle seat?
Sure we've all seen them. Those strange recumbent bicycles. And we've all stared at their owners like they were out of their minds. Well, they probably are out of their minds, but recumbent riders don't get sore butts or backs like the rest of us. Recumbents are just as fast as road bikes as far as I can tell, which make them good choices for fast club rides.
Do I live where there are an abundance of steep hills?
You might want to consider a sport bike -- a road racing frame with a triple crank and, often, more relaxed geometry. These two enhancements are simply more physically forgiving. The lower gears you get from adding a triple crank will save your knees by allowing you to keep a higher pedaling cadence up those annoyingly steep hills. This is probably a requirement for those cyclists with bad knees or a few extra pounds to carry around. A more relaxed geometry will make your ride more comfortable on long rides and will make climbing hills easier. You pay for these benefits by losing some aggressiveness. You won't be winning any sprints on your sport bike, but you'll still be able to walk at the end of your next century .
Do I want to ride with a full-time partner or child who doesn't ride at my level?
Then you should get a tandem. They are not cheap, but it may be your only hope of keeping up with your wife (or husband) or pre-teen child. Of course, before shelling out the big bucks for a tandem, you have to ask yourself, "Can I really stand to be attached to this person for hours at a time? Will they cooperate? Do I trust this person to be my tandem partner?" Hey, half of the fun of bicycling is "getting away." If you want some time alone, you're out of luck. However, tandems can bring people closer together much more than just sitting on the couch together watching television. And, best of all, nothing goes faster than a good road tandem on the flats and especially downhill! Keep in mind that you'll want to purchase a road tandem (one with 700c wheels) rather than an off-road tandem (with 26" wheels) to get those speed advantages.
The off-road bikes might look cool, but where are you going to ride that monstrosity off-road?
Will I primarily take leisurely rides on paved streets or bicycle paths?
If you just want to relax on your bike on short rides at a comfortable pace, you might want a hybrid. They're not so great off-road and not so great on fast road rides. However, you usually get to sit more upright and have lots of small gears for riding easily. You might want to trade in the stock tires for something with less tread and more air pressure to increase your riding efficiency.
Am I a kid who doesn't need an expensive mountain bike to destroy?
You can buy an inexpensive BMX bike to beat up that will accommodate your smaller size.
Do I just want to look cool riding on the sidewalks and bike paths in the cool part of town?
Then get a new piercing and hop aboard a groovy cruiser. They look like your grandmother's old Schwinn, but these days you can put fancy componentry on that funky little frame, including various internally shifting rear hubs. This is a bike that just looks like it belongs riding up and down busy city streets (wear a helmet anyway, dude!) After all, if you don't feel look and feel great on that bike, why bother?
Source: About: Bicycling- Beginners Bicycling website/ photo courtesy of tradebit.com