Anakin is presented as wanting power and status. It was rather overshadowed by all the melodrama about Padme, but we see him whining in Ep III about how badly he wants to be given the rank of Jedi Master and a seat on the Council. In Ep II, he tells Padme that "someone wise" should rule the galaxy as a dictator. Finally, as mentioned in DavRob60's answer, there is his rant to Padme in Ep III about how he can overthrow Palpatine and the two of them can rule the galaxy.
IMO, Episode III would have been much better if this motivation was played up. As Ep III opens, Anakin is a hero of the Clone Wars; but once peace arrives, he will be only an ordinary Jedi Knight.
At best, Anakin will slowly rise through the ranks of the Jedi. It will take decades for him to reach a really senior position, and Yoda will continue to outrank him for the foreseeable future. But it's questionable whether he will be promoted to the Jedi Council at all. The Jedi Masters distrust him, because he's not a team player and too passionate and ambitious.
Most importantly, there is his secret marriage to Padme. Maybe the Jedi have been turning a blind eye to it because they need Anakin for the war, but they will punish him when the war has ended.
So, Anakin is looking at a future as just another Jedi, and either hiding his marriage for the rest of his life or being disgraced if it is found out. Palpatine offers him a way out, in which he can have the power and glory he craves, and he and Padme can live openly as a married couple. Frankly this would have been a lot more interesting than all the nonsense about visions of Padme's death, but it's not what we got.
As for the scene in ROTJ, I agree Vader is protecting Luke as much as the Emperor. But I'd add that Vader has been trained to obey the Emperor for the last twenty years, and it's a hard habit to break. As he says to Luke on Endor (approximately): "It is too late for me. I must obey my master. If you only knew the power of the Dark Side."
I'm speculating here, but it may be that the Emperor can use the Dark Side to condition Vader into remaining loyal. After the events of TESB he might have suspected Vader was planning to betray him, and stepped up his use of these powers. For Vader to break his conditioning and defy the Emperor to his face was extremely difficult.