I don't have a very good track record with indoor plants. I've proven myself to be a fairly good gardener, but potted plants tend to wither away under my supervision. This is partially due to the fact that I travel many weeks out of the year, and partially due to the fact that I take weird pleasure in letting my plants get really thirsty, and then watching them spring back to life when I finally water them. I'm kind of an asshole to my potted plants.
A few years ago I discovered the perfect plants for me. I believe all of these guys fall into the "succulent cactus" category. They are hardy, like a normal cactus, but they are minus all of the prickliness of their spikier relatives. In fact, these plants are down right plump, and their "leaves" have an interesting fleshiness that I find very appealing. No matter what I do (or don't do), the succulents refuse to die, and only a small amount of tender care has produced great results. Succulents are unassuming, hardy, and all around charming little plants. You should get some.