It looks like a Dracaena.

Elsie

Thank you so much, after a little digging I found that it is a dracaena marginatas. Now to get people to agree to proper care for the plant. One says one thing, another, something different. I just hope that I don't kill it and one day the leaves will again stand straight and not droop so much. Thank you again.

What you do is read up on what several websites say about their optimum growing conditions and ask yourself if you are providing them. Yes, there will be lots of variation, because this is a plant that will do well under a pretty wide range of conditions. If 5 people here in the GardenWeb post about the care of this plant, you are likely to get 5 different points of view.

Don't forget to consider the type of potting medium, as the health of the root system is KEY to the health of your plant.