A keel balances a monohull in the water. The keel is a large flat shape with a aerodynamic leading edge. They come in six general variations: full, fin, bulb, wing, centerboard, and canting.

Full
A full keel by definition runs the length of at least 50% of the hull. The forward edge curves vertically while the aft edge often connects to a rudder. The main advantage of a full keel are safe grounding and directional stability.
Safe grounding means a full keel is safer when you lie on hard ground. Whether along the coastline or in travel lift slings, the full keel provides a strong, stable balancing point for the hull. A full keel boat will not tip on its bow or stern. When you ground then, the boat will lay on her side in shoal water and take less damage. In a travel lift, the full keel is easier to sling with the longer keel line. Blocked up on the hard, the full keel provides a line of balance. Be it an unintentional or intentional grounding, a full keel has more stability.
A full keeled boat points well when in the water. It has good directional stability. Put the boat in a compass direction and with a properly designed full keel is likely to stay pointing in that compass direction. The full keel has longer waterline length so controls the flowing water more than shorter keels. The water rushes by for a longer distance and smoother flow. Turbulence is less likely to generate forces to twist the boat. The full keeled boat is less likely than a fin to fall off because this smoother flow. The boat has greater directional stability than a fin.

Fin
By a fin, I refer to a simple deep keel that’s length is less than 50% of the hull. The fin is flat and sharp edged, shaped like a shark fin. A fin keel is fast. The fin keel has less wetted surface area than fuller keels and drafts more. The deeper draft makes the boat sail great. In general, the deeper a sailboat drafts, the faster she is. For racing and performance cruising, the fin keel is king. Reading threads in Sailnet, you’ll see Jeff_H as a great proponent. His articulate posts are worth a postmodernist’s read.
Bulb
The bulb is a shoal draft fin keel. Basically, you saw off a deep fin keel and attach a torpedo shaped bulb of lead to the keel bottom. This shallower keel is a compromise between the performance of a fin but the realities of cruising in the Bahamas, Cheasapeake Bay, and other shoal water holes. Often makers these days produce shoal and deep versions of their designs. Hylas, Valiant, and Tayana come to mind. If you plan to sail in shoal waters, they recommend a bulb keel but otherwise you will enjoy the deep fin keel. As a side benefit if you do ground on a soft bottom and sink in, the bulb keel is the easiest to free. The bulb does not stick way down into or catch the muck like other designs. The bulb at the bottom plops out easily.

Wing
The wing is another shoal alternative to the deep fin. Instead of one bulb at the keel bottom, the wing has two bulbs laterally offset and connected via lead airplane wings. Or the wing is a thick foil of lead without bulbs. The wing has better performance than the bulb because she reduces tip vortex turbulence. The draft can be even less. Because the two bulbs are offset they do not mess with the leading keel edge and generate turbulence like a simple bulb keel. As a drawback, the wing is the most difficult to free if you slide into muck. The wings have a way of gripping down into the bottom. Wing keels are seen on Catalinas and Irwins.

Centerboard
Another shoal idea is the centerboard. The centerboard keel has a base keel with a dagger than rotates downward. When the water is deep, you stick the centerboard down. When shoal, you sail centerboard up. You get the performance of a deep keel and the manuverability of the shoal – a perfect idea, right? The drawback is maintenance with the centerboard. As with any moving part, problems arise. The centerboard has to be maintained.

Canting
The latest and oddest in performance is the canting keel. A canting keel mounts on a hinge and when the boat heels, racers hydrolically rotate the keel to windward. Rotating the keel away from your heeling direction, generates force which both rights the boat and propels her forward. The downside is the maintenance and complexity associatied with the canting keel. It is the future for racing but not perfected yet. I saw the 65 Windship, Procyon, of the Harken brokers which has a canting keel (and bipod mast to boot). “How do you like the whole canting keel thing?” a fellow broker asked. “It’s great. Oh boy is she fast.” The owner loves the canting keel but of course there are downsides of maintenence and the inherent risk of failure with any complex system. Every sailboat decision is a trade-off.
Conclusion
The main types of keels are the full, deep fin, bulb, wing, centerboard, and canting. The full is the oldest and slowest while the canting is the newest and most complex. In general, the bulb, wing, and centerboard are compromises on a deep fin to allow for shoal water cruising.
1.) Why not make a canting bulb/wing keel?
2.)Alternatively: bilge keels could be added as is apparent in the above picture: canting bulb/wing keel + bilge keels.
3.) Fixed bulb/wing + bilge keel
Somebody could clinch a thesis on hydrodynamics by quantifying the results of these various combinations.
1.) Why not make a canting bulb/wing keel?
Canting keels generally are bulb keels. The concept of a canting keel is to get as much of the ballast weight to windward as possible. Typically, below the hull a canting keel consists of a strut and a bulb. The strut is generally made as light as possible, while the bulb is made as heavy as possible. The bulb is typically shaped to minimize drag while getting the ballast as low as possible. Typically this is a flattened torpedo shape.
There is no reason to combine a canting keel with a wing keel. Conceptually, wing keels generally are about increasing lift while minimizing vortex induced drag. Since the canting keel does not act as a foild providing resistance to leeway,adding a wing would do very little, but also wings are very sensitive to having a proper angle of attach and the nature of a canting keel is that the angle of attach would vary widely.
2.)Alternatively: bilge keels could be added as is apparent in the above picture: canting bulb/wing keel + bilge keels.
Canting keels are generally combined with dagger boards which are angled outboard and which are raised and lowered on each tack. These dagger boards are the foils which provide the lift resisting leeway. These are generally not part of the ballasting system. If they were fixed in place, the added drag of having two foils, plus the canting keel would offset the advantage of a canting keel except in higher wind conditions.
3.) Fixed bulb/wing + bilge keel
Again, the whole driving force with keel design is to maximize resistance to heeling, and maximize lift while minimizing drag within the intended draft of the vessel. Bilge keels generally start out with a lot of drag for the amount of lift and stability that they produce. Their sole advantage has nothing to do with sailing ability, as much as it does with produce a shallow draft boat that stand on its own legs when the tide runs out.
Adding a fixed bulb or wing keel to bilge keels would only increase the drag and would add minimal lift due to the interference to the flow caused by the turbulence of the three foils on each other when operating in close proximaty.
Somebody could clinch a thesis on hydrodynamics by quantifying the results of these various combinations.
Not Likely
I would strongly disagree with the Conclusion above. While it is true that full keels are the oldest form of a keel, it is a big mistake to think they offer more stability than a bulb keel. In a general sense, a properly designed bulb keel locates its ballasting more efficiently than most full keels. In practice, pound for pound the righting forces are enormous for the average bulb keel as compared to a typical full length keel. I would also somewhat disagree with the generalization that a bulb keel is a compromise on a deep keel to allow for shoal water cruising. Bulb keels optimize righting moment for a given draft which is why bulb keels are the current norm for deep draft race boats as well as shallower draft performance boats.
You also do not address keels with cut away forefoots, and forward placed stern posts that were so common during the CCA era. These offer almost none of the virtues of a full keel or fin keel, with almost all of the liabilities of both.
Respectfully,
Jeff