Why does David??

Well, it didn't turn out to be so dumb, did it? There are countless reasons why he may want to have Shaw's cross on his person. I don't want to spoil your fun by giving you a few possibilities that I'm sure you can come up with if you put your back into it.

he is a clepto just like call/rider lol

@belladonna If David8 is a kleptomaniac, then he is human after all, a robot with psychological problems?

maby he is a programmed kleptomanic, with pscychological problems. its the future, everything is possible

perhaps, we do know he has the problem of pushing buttons... maybe he is OCD too! i would hate to be in an elevator with him....

Throughout the picture, David knows more than we're told he does. He probably wanted to make a point with the cross, and was suspecting that the rise of Christianity might be a sensitive topic to discuss with the engineers.

Imagine if Shaw comes to the engineers and asks why they created her, only why does she carry that cross? What is she saying she believes? David may have put the cross in his pocket, knowing Shaw was coming with to speak to the surviving engineer, and may want it back, but this film is challenging fundamental issues of religion and creation. The engineer could have killed them at the end because he was offended they tried to create an android in his image, and 2,000 years ago they were trying to go to Earth to wipe us out? Why? Maybe because of Christ. I bet you the engineers are fallen angels, and the sequel will go into this.

Actually the answer is found in the Prometheus Special Features Disc. David was written specifically to do things that were morally ambiguous or morally questionable. In pre-release media it's established that the David8 model was partly designed to do things that humans may find morally or ethically challenging. As such David placing the black glupe (it's called glupe not goo in the extras on the DVD) in Holloway's drink was such an action. Fassbender explains that David was meant to make the audience question the "why" of his actions ... Whose side is he on? Did he do that deliberately? So in answer to the question of why did he pocket Shaw's cross? It's probably the same reason a kid burns ants with a magnifying glass, or rips the wings off a butterly ... In this sense it's a symbol ... If I take away her cross, does she lose faith? He's not bound by our notions of faith, morality, ethics, or anything ... Everything he does in this film is designed specifically to observe the response to it ... It's why he's such an ass!

I think it's half and half. David definitely has that cold calculating side and is conducting experiments-- gathering data. But we're also told he can understand emotion and doesn't like war. In short, I think he means what he says on some levels sometimes and is actually experiencing some emotion about all his unethical acts as he commits them. David was actually exhibiting complex emotions with his sarcasm and a form of double meaning hiding the true emotions in an obvious way when he says "I didn't think you had it in you". Shaw knows he's lying on one level. But David actually could be glad her survival instincts allowed her to overcome Weyland's plan he was forced to carry out, sometimes in his own particular way; His own interpretation of the orders... what he chose to believe "try harder" allowed him to do. David shows some anger towards Holloway and this influences his decision to infect him. David is a lot like Pinocchio, it's almost like we as the viewer can almost tell when he's lying or not being quite as accurate or helpful as he could be. David may not have morals or ethics and can't combine his logic with emotion; but he's slowing experiencing his emotions and becoming more real I believe. I think David was under Weyland's programming for a lot of it and learning things through his experiences-- however he had already developed a dislike for his parents because of his programming. Doing the unethical acts may help his emotional understanding form a sort of twisted form of conscience and free will as he combines logic with intuition/emotions, like how Shaw combines Science and faith/belief. Holloway could be right, David could have been made "too close". David might be becoming more ethical and real, more like a "real boy", more like a dark version of Pinocchio as he continues his adventures. Holloway was a jackass for calling him "boy" so much. This is could be a subtle Pinocchio reference and a clue to the idea that David may be becoming a "real boy". In this story he's been made real by his father who doesn't believe he's real or has a "soul", however, David's a puppet who becomes more than a puppet and starts pulling the strings. Look at the disappointment on Fassbender's face when Weyland says he doesn't have a soul. Maybe he doesn't have a soul, or any morals/ability to understand the effects of his actions at first and it takes David a lot of experimenting before it becomes apparent he has switched to the "good" side and ends up sacrificing himselves for the greater good.