Here is a pretty extensive list of safe plants to have around birds. If you like to have plants in your home you may want to consider printing out this list.
I saw peas and potatos listed in the unsafe plants. I wonder if that means the plant itself (the leafy part) or the part we eat? River has had frozen peas lots of times and really likes them, but I have seen no ill effects. He's never had potatos, but I've read (on here I belive) of people giving small bits of mashed potatos to birds.