If you overwater houseplants, most will suffer or outright die. For most houseplants, it’s best to let the soil dry slightly to the touch before watering them again, but there are a few kinds that enjoy perpetually moist conditions. These include ferns, palms, dumb cane (Dieffenbachia, shown), and even the spider plant (Chlorphytum comosum), though all of these appreciate a winter rest period where their soil is allowed to dry slightly between waterings.
If you tend to overwater houseplants, your best bet may be the umbrella plant (Cyperus involucratus or C. alternifolius), which has tall stems topped with grasslike leaves arranged something like an umbrella or a helicopter’s blades. This plant likes damp soil and bright light. It’s also easy to propagate by simply snipping off the “propellers” and sitting them in a dish of water until they sprout roots—a nice experiment for your young indoor gardeners.
You might also try moth orchids (Phalaenopsis) and even Christmas cactus, provided you keep them potted in a loose, chunky potting mix, such as one based on bark chips. These plants grow on the branches of trees in their native rain forests, gleaning moisture as rain showers through them daily. They, too, prefer a winter rest after flowering, however.
Air plants (Tillandsia) may work for you overwaterers; these have inefficient roots and need to be frequently misted with a spray bottle because they take up moisture through their leaves. Certain other kinds of bromeliads form a reservoir in the middle of their leaves, which should be kept full of water.
Finally, you may try some tricks to help your plants dry out quickly and therefore require frequent watering regardless of their type. Use clay pots, which promote quick evaporation. Remember that small pots dry out much more quickly than large pots. Warm air also hastens drying. If a plant seems too swamped, remove it from the pot and wrap the root ball in newspaper until the excess water has been drawn out, changing the paper as it becomes saturated.