I've heard and seen a lot of controversy on this, so I thought I'd share my experience. I have lucky bamboo in my 20gL and it's been there for a month now. There is visible growth and it doesn't seem to have any ill affects on the fish or water parameters. The key, though, is to make sure the stalks go out of the water and that no leaves are in the water. Once submerged, the leaves will not grow underwater and the stalks will grow roots all over the place and stretch down towards the substrate (I've found that gravel is best). The growth that I've seen in this plant in just a month is incredible compared to the year I've had it. This plant was 4' long before I cut it down and put it in my aquarium, so it was quite big. I would suggest starting out with a bigger plant since it's easier in the long run. So, here are some pictures of my bamboo.
See the noticeable leaf and root growth?
Note: on the large group of stalks in the back, I did use a twist-tie to keep it in place. Depending on the type you use, they can it cannot bother the water/fish. I'm saying this because some of them are plastic, others are paper, and the ones that come with the bamboo are usually gold foil.
Good luck keeping your bamboo!