The Mayflower, for which the ship of the Pilgrims is named, is Epigaea repens. It is better known as Trailing Arbutus. It is a trailing evergreen belonging to the Heath Family with a white flower with a pink center.
Although it is said to be one of the choicest wild flowers of the Eastern United States, it is not a common plant in cultivation despite the many attempts to establish it in gardens. It requires an acid, peaty soil in a shady place, and seems to like association with Hemlock. It is said that the dried leaves are slightly astringent and are used as a tonic and diuretic in much the same way as 'Uva ursi' and 'Chimaphila' are used.
An infusion of the herb was used for treating diarrhea in children by the Cherokee according to an article posted on the Internet by the Brooklyn Botanic Garden (which neither recommends nor condones such use without consulting a physician). It is also the tribal flower of the Ottawa Indians.
The ship Speedwell was also named for a flower, a Figwort also known as Veronica Officinalis.