Many people, after a few tries at indoor gardening, give up, assuming the thumb just isn't green enough. The problem usually boils down to having chosen a high-maintenance plant and giving it low-maintenance care. Thankfully, there are also a lot of carefree, easy to grow indoor plants.
The philodendron is a hardy, tropical vine that loves to climb the walls. You can put it in the sun or in the shade and it won't matter, it will still thrive. Moist soil is the only demand from this plant and, even with that, it can be quite forgiving. Fertilize the heart-leaf philodendron once a month with a houseplant fertilizer, diluted to half the recommended strength. Remember to always water a plant prior to applying fertilizer. As with most house plants, cut back on water and fertilizer during the winter months.
The peace lily is a very pretty plant that prefers a bit of light, but will do just fine in the darker corners of the home. Allow the soil to dry out before watering and make sure the room temperature doesn't drop below 55 degrees and your peace lily will be healthy. As an added bonus, the peace lily helps to clean the air of potentially harmful gases, according to NASA.
Jade is a very easy plant to grow. It does like light, but it doesn't have to be direct sunlight. Any somewhat sunny window is fine. If you pot it in the correct medium, this is one of those plants you can put on the counter in the kitchen or bathroom and forget about. It needs good drainage, so put some rocks or broken pottery shards or gravel into the bottom of the pot prior to pouring in the soil. A mixture of sand and peat moss is perfect for the jade plant. Take care not to overwater the plant. If the leaves start to shrivel, it's time to water again.
Yes, there are palms that are not only easy to care for, but do well indoors. The kentia palm likes direct light but will tolerate lower light. This is a palm that doesn't need too much water either, just water when the top inch or two of soil is dry. If you are looking for a palm tree that will thrive in a little less light than the kentia, the lady palm might be worth considering. It has similar watering needs and has very limited fertilizer needs--two or three times per year--so it's truly a low-maintenance plant.