Do I seal just the grout or the tiles and grout?
This greatly depends on the type tile you have. If it is a manmade tile such as porcelain, or ceramic, then you don't have to worry about sealing it.

Most natural stone tiles, especially softer or water permeable stone such as marble, limestone/travertine, and slate should be sealed as well. This would ideally be done prior to grouting to prevent the stone from being stained by the grout. It would also be a good idea to use an unsanded grout with natural stone, especially marble because the sand from the grout could leave scratches in the surface.