Here's my interpretation of Vader's motivation (which I thought was everyone's until reading this thread!):
Post Star Wars
Prior to knowing about Luke, Vader dedicated himself totally to the idea of the Empire and power for its own sake.
Once Vader finds out that it was his son who destroyed the Death Star, he stops giving the merest flip about getting revenge from the Death Star. He wants Luke for emotional reasons (the son he thought he'd accidentally killed, Padme's child, survived) and strategic reasons (allied with his son, he can take down the Emperor and become the master, something he can't do given his injuries).
The Empire Strikes Back
He tries to find Luke for himself, using 'revenge for the Death Star' as his offical, Imperial reason. So at the start of ESB, he's 'obsessed', scouring the galaxy for Skywalker. The Empire wants him because he's a terrorist; Vader, privately, wants him because he would be an asset.
Once Palpatine makes clear that he knows Luke is Vader's son, Vader changes tack - he pretends this is news to him too, and so now officially wants Luke so that he can join Vader and the Emperor. Both want Luke for themselves, both want the other to think that they want Luke to be the new part of a triumvirate.
Vader makes a show of wanting Luke for the Emperor - publicly referring to Luke as 'the Emperor's prize'. However, had Vader successfully frozen Luke, he would have had no intention of taking Luke to the Emperor.
During the duel, Vader never wants to kill Luke - he wants to knock him in the freezing pit, for unfreezing under controlled circumstances. He's happy when Luke proves to be talented, but when Luke proves more talented than he expected, injuring him, Vader gets pissed off, stops playing about, and quickly chops off Luke's hand.
Vader comes clean, and makes his - totally heartfelt - pitch to Luke. He is furious when Luke elects to kill himself. When Luke survives, but escapes, Vader is so upset that he can't even bring himself to kill Piett. This is probably the point where he starts to turn back to the light side: his son is alive, his son is talented, he mutilated him in service of a plan which didn't work, his son elected to kill himself rather than join him, his son escaped from as tight as trap as the Empire would ever likely be able to set. He knows he's missed his chance to get Luke on side. So, naturally, his commitment to that side starts to waver.
Return of the Jedi
By the time of RotJ, Vader doesn't know what he wants - he's depressed and given up, which is why he no longer bothers to pursue his own agenda of catching Luke for himself, instead just functioning as the Emperor's puppet. After the conversation he has with Luke - when he tells him 'It is too late for me, son' - the fight goes completely out of him, and he pretty much stops thinking for himself until Palpatine starts electrocuting Luke.