I think it's important to mention that pedals aren't simply "road" or "mountain" pedals, but that there are pedals designed for many different purposes. Most people will classify "road race" pedals such as Look Keo, Shimano SPD-SL, and Speedplay as "road pedals" and most other pedals including Shimano SPD and CrankBrothers will fall into the "mountain pedals".
Road race pedals in my opinion are pretty much what they sound like. They are built for road racing and very little else. They are difficult to walk in, and many people have difficulty clipping into them. This isn't a problem if you are road racing because most likely you will be clipping in and then won't be clipping out until hours later. The shoes designed to work with them are usually very stiff soled and are designed only to be used for pedaling.
Mountain pedals on the other hand have a huge variety of pedal styles and shoes available. Some pedals have almost no platform at all are little more than an axle with a clip attached to grip the cleat. Others have quite big platforms and can be used with regular shoes as well as cycling shoes. There are also pedals with a platform on one side and a clip on the other. Despite the fact that many people use "mountain" to describe these pedals, many people use them on the road, and many of the designs are much better suited to the average road cyclist than a road race pedal would be.
Shoes comes in all forms as well from very flexible shoes or sandals that you could walk in all day to stiffer racing shoes that, while still walkable, definitely wouldn't be good for extended walking.
Shimano also makes pedals called "Click'r" which are specifically aimed at more casual and recreation cyclists. The are designed to be very easy to clip in and out of, while still providing many of the benefits of using a clipless pedal system.