Plants that grow entirely under water are sometimes called oxygenators. They do supply some oxygen to the water during photosynthesis, but they also consume oxygen 24 hours a day through the process of respiration.

They are not necessary in a container water garden, but they can be used if desired, especially if an ecosystem approach is being used for maintenance, where each component of the system is being used. They can be beneficial as they remove nutrients from the water that would otherwise feed algae.

A few of these plants grow mostly under water but often have above water stems that can be very attractive in containers, such as the plant called Parrot Feather.

Wild Celery (Vallisneria sp.) flat ribbon-like, translucent, pale-green leaves. It can tolerate shade, part-shade, and sun in water that is 6 to 24 inches deep.
Fanwort (Cabomba canadensis) Bright green feathery foliage. It can grow in sun to part shade in water that is six to 12 inches deep.
Anacharis (Egeria densa) Dark green leaves, and it sometimes blooms with tiny white flowers that float on the surface. It can grow in water one foot to over five feet deep.
Parrot Feather (Myriophyllum aquaticum) Grows in shallow water, partly submerged and partly floating. Can grow three to six inches out of the water, or it will hang several feet over the edge of water garden containers. Grows in full sun or shade.

Floating plants are great additions to many water gardens. They have root systems that hang down into the water. They filter the water of nutrients that would otherwise help algae grow. They shade the water, sheltering fish and preventing sunlight from benefiting algae. Some floaters such as Water Hyacinth have pretty flowers too. Many floaters, including Salvinia and Water Hyacinths, are banned from several states because they can spread rapidly in natural waterways.

Giant Velvet Leaf (Salvinia longifolia) A small, tropical, floating fern with pale green, round, hairy leaves.
Water Hyacinth (Eichhornia crassipes) A common plant that cannot tolerate frost. Long, trailing roots, balloon shaped stems, and spikes of pale lavender flowers.
Water Lettuce (Pistia stratiotes) Velvet-covered green leaves forming a rosette of foliage that looks like a floating head of lettuce.

These plants have their root systems firmly anchored in the bottom mud, while the leaves and flowers either float on the water's surface or are held above the water. There are several dwarf varieties of both lilies and lotus that are suitable in container water gardens. They all need full sun for best blooming, but some can tolerate a lot of shade, if blooms are not the primary focus.

Hardy water lilies live where the water's surface freezes, but the roots don't freeze down deep in the pond. They only bloom in the daytime and are usually not fragrant. The leaves have smooth edges.

Tropical water lilies cannot survive freezing. They are often fragrant and the flowers come in blue and purple shades that are not found in hardy water lilies. Some even bloom at night. The leaves have scalloped edges and are often mottled in red tones. They require warm water, at least a half day of full sun, and around a foot of water over the crown.

Froebeli - A hardy, red lily that can stand the heat that might build up in a small container.
Joanne Pring - A hardy, miniature, pink water lily with green leaves.
Tetragona - A hardy, miniature, white water lily with red mottling on the leaves.
Helvola - A hardy, miniature, yellow water lily with red mottling on the leaves.
Yellow Pigmy - A hardy miniature that is a prolific and consistent bloomer.
Hilary - A tropical, day blooming, pink water lily with green leaves.
Red Flare - A tropical, night blooming, red water lily with maroon leaves.
Momo Botan Lotus - Grows to a height of 24" with rose blooms July - September.
Wan-er Hong Lotus - Grows to a height of 12" with white blooms June - September.

Depending on the species, some of these plants like to always have several inches of water over the crown of the plant, while others can easily tolerate merely damp garden soil around the roots. Planting shoreline plants in a container water garden should take into account how much water over the root system the plant prefers.

Arrowhead (Sagittaria sp.) Green arrowhead shaped leaves. White, one-inch flowers five or ten to a stalk. Grows from 12-48 inches tall, in sun to part shade, in streams and along shores in shallow water.
Cattail
Creeping Jenny (Lysimachia nummularia). Grown for its ground-cover-like creeping runners that hang over the sides of containers. Enjoys shallow water conditions and tolerates bright, indirect light or partial shade.
Blue Flag Iris (Iris versicolor) Blue flowers in late spring with flat foliage. Grows from 24-30 inches tall and will tolerate full sun to part shade. Tolerates several inches of water over the crown to just moist garden soil.
Houttuynia "Chameleon" (Houttuynia cordata) Multicolored leaves of red, cream, pink, and green. Perennial creeping plant that grows to six inches tall. Grows well in part shade and hangs over the sides of water garden containers.
Lobelia
Dwarf Papyrus (Cyperus isocladus) Green grass-like foliage in an umbrella shape on top of a stalk. Flowers amidst the leaves are not showy. Grows 12-18 inches tall and tolerates sun to part shade. Needs to stay wet and will not tolerate cold weather.
Water Canna Many flower colors are borne on top of three to five foot tall stalks of wide green leaves. Some have red or multi-colored leaves. Grows in moist soil to three inches of water.
Taro Huge green leaves up to seven feet tall. Tropical that tolerates shade. Grows in damp soil to submerged several inches.
Corkscrew Rush (Juncus effusus) Interesting twisted and curled wiry leaf. Grows to 24" tall and tolerates full sun to part shade. Prefers one to three inches of water over the crown.