Road bikes are fast and easy to pedal on pavement. They are not as well suited for operating off the road. Some people find the "dropped" riding position difficult to maintain, comfortably, for a long time.
Mountain bikes are harder to pedal and slower on pavement. But they have a cushy ride, an upright riding position, and can travel easily on a wide variety of surfaces.
Hybrid or cross bikes are almost as fast and easy to pedal as a road bike, while being upright and comfortable.
Comfort bikes are just that—comfortable. They are less efficient, but sitting on one is much more comfortable and stable.
Cruisers are fun to look at and, when ridden at a relaxed pace, they are ideal for admiring the scenery, exploring the neighborhood or beach.