There are several criteria to keep in mind when selecting plants to adorn a grave site. First, check with the cemetery about any planting rules it might have. Next, look for low-maintenance plants, because you won't always be there to remove spent blooms or prune. Drought tolerance is equally important for the same reason. Consider, too, the mature size of the plants.
If you want to use only one plant that will provide multiple seasons of interest, Sedum "Autumn Joy" would be an excellent choice. Thriving in full sun to part shade, it is drought-tolerant, perfectly sized at 12 to 23 inches tall and undergoes colorful changes throughout the season.
Annuals including as New Guinea impatiens work well in sunny spots. Ordinary impatiens should be avoided, as they are susceptible to downy mildew.
Vinca is a long-blooming annual that's available in a variety of colors and thrives in sun to part shade.
Chrysanthemum 'Matchsticks' lend great fall color.
Pansies will complement the mums until frost and return to fill in spring.