If you have an older home, particularly one that was built in the Craftsman period, beadboard is an excellent and time-appropriate choice. Beadboard refers to a type of wood treatment in which small slats of wood are laid together. If you don't have the time or patience to install these slats, consider purchasing beadboard paneling and nailing it up over a plywood sub-ceiling. This gives you the best of both worlds and simplifies the installation process.
Plywood is perhaps the easiest material to work with when installing a deck ceiling. It is economical and can be nailed up quite easily. But instead of leaving it plain, get creative. You can prime the plywood and then paint it in the color scheme of your choice, add creative stencils, or even stain it to look like much more expensive wood. Just remember to seal it with an exterior polyurethane to protect your artwork.
If you live in an area where the weather is typically quite good, you don't have to shut out the view of the sky. Install a lattice as a ceiling instead of using a solid material. This will help increase ventilation as well as opening up the view above. This lattice comes in either PVC or wood, and you can paint it a different color to make it even more visually interesting. Plus, as long as it is properly supported, you can hang plant baskets from the latticework.
For a Victorian-era house, or if you just want to have a little fun, use faux tin tiles over a plywood sub-ceiling. You can order these tiles plain and then paint them any color you choose, or you can order them in different finishes. Just glue them up over the plywood and you have an instant tin-like ceiling. The foam tiles are weather-resistant and will provide a totally new look for your deck ceiling.