Dracaena fragrans "Massangeana". The "fragrans" refers to the fragrant flowers it produces.
Once established in a consistent set of condition, it can usually stay happy for long periods. It needs indirect bright light, good humidity, moderately watering and temperatures of 20 to 30C, and never below 15C for prolonged periods (although mine went through a period with temperatures down to 10C for a short period).
However, they are very sensitive to sudden changes of growing condition, particularly humidity. Which is the exact problem when you bring one home from the nursery green house. You are not likely to kill it, but some of the leaves will dry off. Just trim off the unsightly leaves, provide as much humidity as you can (put the pot into a water tight container - in the bottom of the container, layer with 2-3 inch of gravel and add water up to the top of this layer. Keep the gravel under water all the time.) Fiind a spot with indirect light (never direct sunlight) where it will not be subject to sudden cold drafts. Once you have found the spot for it, try not to move it. Water well, then allow the potting media to go slightly dry before watering again (I water when the surface of the soil feels and looks dry).
(Our plant reached a height of 15 feet indoors before we had to give it away!)
Here is an excellent webpage on dracaenia:
http://www.briansgarden.com/houseplants/030211h.html