Be very careful not to over-water your plants. Watering once per week usually works well. The safest way to go when it comes to watering, is to know your plants and know the specific growing and watering requirements for them.
The article below, taken from the website, Balcony Garden Web gives a great list of 17 of the easiest and best plants to grow indoors.
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Parlor Palm
Most popular indoor palm variety, it’s an excellent houseplant for almost any situation, it grows even in those dim corners where nothing else will grow. It requires only minimal care and moderate light. It produces clusters of tiny yellow flowers in spring, however, these will not form in low light conditions.
Water only when soil is dry otherwise you’ll kill your plant.
Creeping Fig
It’s a slow growing creeper with small, leathery dark green foliage. Vigorous-growing, clinging, dense branches adhere to any surface and looks enchanting. Let the soil dry out before watering
Umbrella Palm
Umbrella palm is an evergreen ornamental plant, best grown indoors or in shady and a boggy spot in the garden. Many houseplant enthusiasts find this plant easy enough to grow and maintain.
It requires constantly moist substrate – pot should be submerged in water. You can place the umbrella palm pot over the tray filled with water.[/su_quote]
To read the entire article with the 17 best house plants go over to the Balcony Garden Web.