I made my first paddle out of pine 2X6. Its light and since it was for my 4 year old daughter, it didn't need to be the strongest wood ever.

My second paddle was a white water paddle and needed strength and flexibility. I used White Ash (32$) which is the same wood they use for making hockey sticks. Its a good sports wood that doesn't deform or warp with time.

The fact that its a really hard wood (hard to carve too) makes it possible to really thin the edges and narrow down the shaft. Its not too heavy because of that. Its a good strength/flexibility/lightness compromise. It does not get damaged or dinged easily.