Yes, this is fairly common in casual speech, not so common in formal writing.
Note that often this indicates that the speaker considers the statement surprising. In general, if you were, asking a person if they wanted to remain in their present location, you would use the "by the book" construction, "Do you want to stay here?" But if a person indicated they wanted to remain somewhere that you thought undesirable, like some place uncomfortable, or if you expected that they would want to leave, perhaps you thought they were in a hurry to move on, then when the person says, "No, I think I'll stay," you might reply in surprise, "You want to stay here?"
It is used as an alternative to a question in very informal speech. Instead of, "Would you like to stay here, sir?" one might ask, "Ya wanna stay here, bud?" This is especially true as the construction of the sentence becomes more complex. "You guys spoke to anyone?" is not unlikely, because the more formal statement would be, "Have you gentlemen spoken to anyone?", which is several levels higher in formality.