Choosing a paddle these days is a whole lot more complicated from when I started paddling.  First off, I need to limit this discussion to whitewater paddles.  Sea Kayaking / touring paddles have much different requirements.  Paddle lengths are much shorter these days which makes sense since boats are a great deal shorter as well.  The best resource I have found for determining the best length paddle is on the Werner web site: Werner Paddles Fit Guide

I tried out the interactive custom fit questionnaire and the results were dead on.  I highly recommend using this resource – even if you have been paddling for a number of years.  The quiz takes into account many factors such as blade area, shaft diameter, style of boating, and paddler height.

The next consideration is choosing a right hand or left hand control paddle.  Nearly everyone goes with the right hand control and I suggest you do the same.  Besides making it easier to stack, you can easily borrow other paddles if you break yours.

The next decision is straight shaft or bent shaft.  Straight shaft paddles are generally less expensive and give you flexibility in hand placement.  Bent shaft paddles force you to position your hands is the perfectly balanced correct position.  Many also find bent shaft paddles easier to roll with as well.  Some find bent shaft paddles are easier on their wrists as well.

The next decision is feather angle.  In the old days, all of our paddles had 90° offsets.  Back then we also had long paddles (212 cm was pretty common) and long boats (roughly 14').  Boats are roughly half as long and most paddles are under 200 cm.  The preferred feather angle has dropped as well.  In general, feather angles are in 15° increments.  Generally, river runners with straight shaft paddles tend towards 45° or 30°.  When switching to a bent shaft paddle, you will probably want to drop 15° on your feather angle.  Play boaters use much shorter paddles and prefer even smaller feather angles.  It isn't unusual to see play boaters with a zero degree offset.  These are some rough guidelines.  I really suggest trying several different feather angles and run some attainment exercises.  You will very quickly figure out what is comfortable for you.  For more detail on feather angle from a true expert, check out the following article from Jim Snyder: Feather Angle.

The next area to look into is shaft diameter.  Women and small-framed men should definitely look into the smaller shaft sizes.  This will make a huge difference in avoiding hand fatigue and the very common "Death Grip".

Now we take a look at the blade shape, there are many.  Most of the time our paddles enter the water at an angle (instead of perfectly perpendicular).  Paddle blades that are cut straight across used to be for slalom (and some down-river) racers.  Their paddle entry angle was almost 90o and they wanted maximum power out of each stroke.  Typical whitewater forward strokes are more angled  so paddle shapes changed to compensate by being longer on the outside than the inside edge.  A very common shape is called the Slasher design like this one from Mitchell paddles.

Tear drop blade shapes are also very common like this one from Jim Snyder.

There are other shapes as well like Esoteric but most whitewater paddlers choose a blade shape like the ones shown above.

You can also go with a flat blade or a cupped blade.  Cupped blades provide a great deal more power than flat blades and I highly recommend them.

Finally, a smaller blade area is easier on the shoulder with the downside of less power per stroke.

The next factor to consider is how heavy and durable is the paddle.  This has a lot to do with materials used to construct the paddle and quality of construction.  The best paddles in so many ways are wood.  Wood is warm, extremely durable, easily customized, reasonably light weight, and can be repaired.  Good wood paddles are also the most expensive choice but not as much as you would expect.  The next choice is fiberglass or carbon fiber paddles.  Many of these are very light and quite strong as well.  You get what you pay for, good glass paddles should last between 5 - 10 years - cheap ones a year or two.  Plastic paddles are also available.  Plastic blades are quite cheap but have an awful amount of blade flex which means serious loss of power.  Avoid plastic blades and metal shafts.

 Two great paddle brands are Werner: Werner Paddles and Advanced Technology (AT).  Expect to pay from $250 - $500 for new fiberglass paddles.

There's only one good wood paddle maker left these days: RivrStyx Paddles. PA Jimi Stick as the are affectionally know as will cost $650 but is a lifetime investment.

Used paddles are often available starting at $100 (sometimes less).

When you purchase a paddle, definitely put your name and contact information on it.  I also recommend wrapping bright colored duct tape in the middle of the shaft on dark colored paddles.  Both these practices will help others in reuniting you with your paddle if you swim and lose your paddle.