From the Convolvulaceae Family is the Genus Ipomoea which has over 500 species. Ipomoea is usually associated with Morning Glory's but there is so much more and not all of them are vines and climbers!
Feel free to add your own but please name the species.
Here are a few that I grow ... I'll start with the more common ones.
I. nil - Fujishibori and Shidare Morning Glory
I. purpurea - Peppermint Twist and Amomurasakihigeshibori
I. sloteri and I. lobata - Apricot Candy and Spanish Flag
I. carnea - Bush/Tree Morning Glory and I. alba
I. aquatica and I. cordatatriloba