Three have leaves with stalks attached to the middle of the lower surface. These are found only on the coastal plain.
Hydrocotyle umbellata, Many-flowered Pennywort
The inflorescence is a simple umbel.
Hydrocotyle verticillata, Whorled Pennywort
The inflorescence is a spike with flowers in whorls.
The individual flowers are stalkless or nearly so.
Hydrocotyle prolifera, Whorled Pennywort
Very similar to H. verticillata, but the flowers have distinct stalks.
Three have leaves with stalks attached to the edge:
Hydrocotyle sibthorpioides, Lawn Pennywort
The inflorescence is above the leaves; the individual flowers are stalkless. Alien.
Hydrocotyle americana, American Water-pennywort
The inflorescence is stalkless. Status uncertain.
Hydrocotyle ranunculoides, Floating Pennywort
The inflorescence is below the leaves, but does have a stalk.
Sources: The Flora of Delaware, Manual of Vascular Plants.