The most important reason is that the Emperor craves power. Vader was older, and is eventually defeated by Luke. Clearly he has lost his edge, so a younger apprentice who is just as, if not more powerful than Vader, would prove advantageous to the Emperor.
Another, lesser known reason which is not addressed in the movies, but stated in many novelizations, is that Vader's ability to use the Force was greatly reduced upon suffering the injuries which confined him to his survival suit. Therefore, Luke, being the son of Anakin, one of the most powerful Jedi known, would definitely be more powerful, inheriting his father's abilities. As Lucas states in the "Making of" book for the third prequel, Revenge of the Sith, the Emperor "will ultimately be disappointed in Anakin," and will eventually see Luke (and possibly Leia) as an opportunity to obtain a more powerful apprentice.
A third reason which can tie in with the first two is that the Sith habitually follow or are afflicted by "the Rule of Two", a name given to a concept expounded upon by Yoda at the end of the first prequel, The Phantom Menace: "Always two there are, no more, no less: a master and an apprentice." This is due to a Sith Lord's extreme inclination to be possessive of other individuals amidst having obsession with power; and due to competition and betrayal accordingly. (The value that anybody has to a Sith Lord cannot be peacefully shared with a third party.) To have Luke and Vader as his apprentices, especially considering they were father and son, would definitely increase the chance that they would betray and kill the Emperor. Vader even proposes this idea to Luke, in The Empire Strikes Back, though that could have just been a ruse to coax Luke to the dark side of the Force, promising him secondary rule of the galaxy. He also suggests overthrowing the Emperor to his wife, in Revenge of the Sith, and ruling the galaxy with her, which was only shortly after he had turned to the dark side.
Also; in the Expanded Universe, the Rule of Two involves a provision of which the Emperor was not fond. As the story goes, the Rule of Two came about after thousands of years of the Sith being in power. The Dark Lords of the Sith were vast and there was an unspoken tradition within their ranks that the apprentices would at some point try and kill their masters. Eventually this imploded and the Sith all but destroyed themselves due to the constant paranoia and scheming between masters and apprentices. Eventually Darth Bane initiated the Rule of Two allowing only one master and one apprentice. The idea being that after the apprentice's training was complete, he would challenge his master in open combat. If the apprentice won the duel, he would strike down his master and claim the title for himself, then find his own apprentice. On the flip-side, if the apprentice lost the duel, he was unworthy of the title of Sith Master, and the master would find a replacement; the idea being that no matter what, the Sith would always become stronger with each master and apprentice. Clearly the Emperor was not fond of Bane's idea, because he manipulated Anakin/Vader in such a way that Vader never found a sincere motivation to overthrow the Emperor after it was thought that his wife and his child were killed. Vader's only desire was to become more powerful through the dark side of the Force. So the Emperor only gave him small bits of training over the years to keep Vader enticed. The Emperor then gets Vader and Luke to duel each other, the victor being intended to be the Emperor's apprentice.