Most plants evolved to grow in soil but some varieties will also grow in water anchored by stones. Many of these plants are readily available and well-known. One of the downfalls of growing any plant in water with stones is that bacteria in the water can multiply rapidly, which turns the water cloudy and makes it smell unpleasant. A teaspoon or two of the type of granulated charcoal used in aquarium filters added to the water will help keep it from turning cloudy and developing an unpleasant odor.
Any house plant enthusiast who has ever cut back an English ivy (Hedera helix) and put the cuttings in a glass of water will confirm that English ivy does indeed grow in water, with or without stones. Including stones in the container will help anchor the plants and keep their leaves out of the water. Stones will also help to keep them from tipping over as they grow larger. When they have put out enough top growth its weight can cause them to tip over and pull their roots out of the water.
Vining indoor Philodendrons (Philodendron cordatum and P. micans) can also be grown in plain water, with or without stones. Because of their rapid growth habits, including stones in the container of water is beneficial to help anchor them and keep the roots in the water as the top growth becomes heavier and more lush.
Paperwhite Narcissus (Narcissus tazetta) is a tender bulb that is forced to bloom indoors in temperate areas. They can be forced in pots of soil, but are often found for sale in garden centers already planted in decorative pots filled with pea gravel or small decorative stones. The stones are necessary in the case of Paperwhites because plain water will not support the weight of their stems, leaves and flowers. The stones effectively act as soil and anchor the plants. Keep the level of water just below the top of the stones.
Special glasses are available in which to force Hyacinths (Hyacinthus nonscriptus) in plain water for indoor blooms during winter. The shape of the glass holds the bulb so that only its lower third is under water. The same thing can be accomplished using stones. Fill a watertight container to within an inch of the top with small stones or pea gravel. Insert the hyacinth bulbs into the small stones or pea gravel so that only their bottom third is buried. Check frequently and add water as needed to keep its level just below the top of the stones.