Q:

What are the pros and cons of plastic and aluminim vs wood vs composite paddles for canoeing?

There are three main types of canoe paddle materials,

Wooden paddles.
Plastic paddles with aluminum handles.
Newer composite materials (fiberglass, carbon)

What would be the pros and cons of each type of paddle material for canoeing?

A:

Wooden paddles are heavier but have a very nice feel to them, they can be expensive.
The flex in plastic blades can mean you lose power and the blades can flutter under heavy load. Aluminium paddle shafts aren't that nice to hold in the long run, especially in the cold. These tend to be the cheapest option.
Carbon blades are usually light, stiff, and usually really nice to handle if you get good ones but you'll be paying for what you get. Easily 10 times the price of a plastic/aluminium paddle.
On a personal note, Carbon/Carbon-Aramid are my preference for kayaking, but wood for open boating, there's just something comforting about wooden paddles.

A:

I've used wood, fiberglass and Mohawk paddles.
My preference is for wood.  A good blade can be made of ash or spruce.  The latter will have a thicker shaft that may be uncomfortable for small hands.
Wooden paddles will break.  In 30 years of canoeing I've snapped about 6.  Once in a rapid.  That got exciting, while I fumbled for our spare.
Wooden paddles will split from abuse.  Sand wedged into the tip can open up the grain, which then creates a small crack that grows.   A square ended paddle can be easily protected with a bit of aluminum sheet metal and 4 rivets.  
Wood paddles need the occasional light sanding and a coat of marine spar varnish.  If you don't put tip protectors on them, linseed oil the tip a week before the first trip of the season.  This will slow down the splitting.
I used a bent shaft fiberglass paddle for a day.  My overall impression was that it had no soul, and I found it heavy.
Mohawk paddles have an aluminum shaft and ABS blade and grip.  Talk about no soul.  However they are light, and close to indestructible. Lots of rental fleets use them for this reason.
One downside of aluminum shaft paddles:  The aluminum rubs off as a very fine powder staining your hand black.  Spray painting the shaft with a metal enamel eliminates this problem, and makes your paddle stand out from the crowd.

Other choice factors:
A longer narrower blade is somewhat more efficient, but requires a different motion.   
A beavertail (round tip) is quieter, and easier to not splash yourself.  
A wider blade makes it easier to move a pile of water in a hurry.  A shorter paddle is less likely to catch the top of a wave.
I preferred to have two paddles:  A shorter paddle (about 4' 8") with a large wide blade for rapids and stormy lakes, and a longer paddle (about 5' 2")  with a longer, narrower blade for cruising.

