I've got quite the collection of indoor plants, and have had varying levels of success with lots of different species/varieties. Out of the dozens of plants I bought, I don't think I've ever seen a spider on one.
Dt is right about the peace lily. It is very easy to maintain, and it actually doesn't need much light. I have one of mine in a corner near a north facing window, where it gets no direct light, and it does fine. It doesn't flower as much, but otherwise does well. Other species that are easy to maintain:
Dieffenbachia: Pretty, easy to maintain, grows fast, but poisonous to children and animals. My cat, though, never tried to chew it, unlike many of my other plants. Does well in medium light (doesn't need window placing).
Crown of thorns: Hardy survivor-type with thorns and pretty pink flowers. Doesn't need much water, so you won't need to ask someone to water it if you go on a trip.
Orchids: the phalaneopsis types are actually quite easy to maintain. Out of direct sun, watered three times a week, will do quite well. The potting mix has to be just right, though. Ask me for details.
Spider plant: possibly the hardiest of plants, and super easy to make more from the little plantlings that the mother plant produces. One of the best for removing formaldehyde from the air, according to NASA. Please note that it has nothing to do with spiders, nor does it look like a spider. It's just a name, tissot!
Bamboo: does much better in potting soil than in water, which is how it is usually sold.
Dracaena marginata (Madagascar Dragon Tree): easy to maintain, tolerates all kinds of conditions, easy to propagate.
Monstera deliciosa (Swiss cheese plant): super easy to take care of, likes shade, grows like crazy, looks amazing.
Hybiscus: lives happily in sunny location, but wants lots of water. Beautiful, huge flowers appear every spring.
Here's an article on taking care of your lucky bamboo:
http://www.flowershopnetwork.com/pages/newsletter/NewsletterJuly2003.php