Road bikes are designed for performance on (mostly) well paved roads. They are the lightest weight of the 3 categories, have the shortest wheelbase, lowest bottom bracket, and the steepest headtube angles. These geometry features allow the bike to react to rider inputs quickly and to have a low center of gravity which is beneficial when turning.
Wheels are almost invariably 700c - sometimes smaller wheels are used on very small frames. Tire sizes will typically vary from 20-25mm width but the most common width is 23mm, thus the 700x23 that you'll often see. Road frames can be made out of just about any material but the most common ones that you'll see are aluminum for budget oriented bikes and carbon fiber for high end bikes.
Gearing will be the highest and narrowest on this type of bike. Road bikes are designed to carry the rider and his/her water bottles and not much else, although some are drilled for fitting racks - usually on the less expensive side.
Road bikes still make great commuters if you want a light weight, fast reacting machine to get from point A to point B.
Touring bikes are designed for long, multi-day excursions on the road. They are usually the heaviest bikes of the bunch as they are built for durability and to carry a lot of stuff beyond just the rider. They will maintain a relatively low bottom bracket but the wheelbase will be longer and the head tube angle slacker when compared to a road bike. This adds to their stability, especially when fully loaded.
Wheels are often 700c but many are actually designed for 26" - some will accept either, though this will make for a higher BB with the larger wheel. Stock tire sizes will run wider - usually 28mm or above. This makes of a more comfortable ride since the air pressure can be dropped.
You may see touring bikes made from other materials, but the most common is steel due to its forgiving nature and durability. Drillings for back and front racks are standard, and drillings for extra water bottles are common.
Gearing may be a little lower, but will certainly be wider on a touring bike. Sometimes mountain bike components are used for rear gearing to give the rider extra low gearing. This is very welcome when ascending with a fully loaded touring bike.
This type of bike makes an excellent commuter as it is stable and when fitter with racks/panniers gives you lots of places to put your stuff besides on your back.
Cyclocross bikes are designed to travel both on and off road. Cyclocross is actually a race discipline that evolved as something for road racers to do in the off season, but the bikes have become very popular outside of racing due to their versatility. Cross bikes will typically be heavier than a comparable road bike but lighter than a comparable touring bike. The wheelbase will be in between that of a road bike and a touring bike while the bottom bracket height and headtube angle could be on either side of that of a touring bike depending on the manufacturer's philosophy.
Wheels will be 700c and tires will typically range somewhere in the 30-40mm width range with small knobs to grip loose surfaces as opposed to the slicks you'll see on dedicated road tires.
Frame materials vary widely just as with the other bike types, but for high end cyclocross frames carbon fiber is becoming a more prevalent material. Aluminum and steel are also common, especially amongst mid level bikes and below.
Traditional cyclocross gearing is a little odd as they typically come with a very close ratio double crankset but this may be compensated for by a wider cassette.
Race dedicated cyclocross bikes may have drillings for water bottle cages in the front triangle though you'll often see them with no bottles mounted so they don't get in the way of shouldering the bike over obstacles. On the other hand, many cross bikes are drilled for racks since they can double as a touring bike due to the similar geometry.
Cross bikes make wonderful commuters due to their versatility and durability. You can often run racks or not, and swap the knobby tires with slicks should you so choose.