There is a product available (I think it could be duplicated much cheaper) that is similar to corrugated fiberglass or plastic panels. It is set to a slope under your deck joists and it attaches out away from the house to a gutter system at the end of your deck. It is white and brightens the area under the deck and takes the rain away.

M*nards sell it.

Here are 3 links for you for "under deck" solutions.
www.dry-b-lo.com www.undercoverdecks.com www.dekdrain.com

You could also look at using vinyl & fibreglass decking that is applied to 3/4 t&g ply I have used both with success each having their own advantages. Do an internet search for those, and if you have further questions if they interest you just ask.

You can use a sealed concrete, look at our site's Greenvalley Project, I used that application for that deck.

Then there are a few composite (mostly injection molded rather than Trex style of wood/plastic mixtures) types of decking that can be used as well, these interlock and provide a water seal.

The higher end you would look at a t&g (tongue & groove) applied & sealed fir or ipe for example.

Alter Eagle Construction & Design