I've got two legs from my hips to the ground And when I move them they walk around And when I lift them they climb the stairs And when I shave them they ain't got hairs!
In Rosencrantz and Guildenstern Are Dead, Act 3 opens (in darkness) with the sound of waves, creaking timbers, people shouting things like "Hard a-port!" and possibly a sea shanty. "When the point has been well made and more so", as the stage directions put it, Rosencrantz observes "We're on a boat." He then follows that up with "Dark, isn't it?", at which point Guildenstern surprisingly claims the title of Captain Obvious from him by countering "Not for night. Dark for day." (They have no idea what time it is.)
In Urinetown The Musical, this is rather common, with examples including constant reminders that the Fax/Copy Girl's job involves faxing AND copying, and the secret hideout bearing a large, lit sign reading "SECRET HIDEOUT" - With the police pointing to the sign as evidence of how hard it is to find. But the all time winner has to be the reveal of The Twist:
Ms. Pennywise: Hope is my daughter!
Crowd: *small gasp*
Ms. Pennywise: AND I AM HER MOTHER!
Crowd: *HUGE gasp*
The Musical version of The Wedding Singer actually contains the lyric "People called him the wedding singer. He sang at weddings and so the name was apt."
Shakespeare's characters sometimes don the captain's braid, but often it's because of the limitations of the Elizabethan stage. To paraphrase another page on this wiki, if your actors are in the middle of a sword fight but they're only pretending to be using swords, it's probably helpful if the victim grabs at his chest and cries "O, I am slain!" so the audience knows what happened. Also, if your only set decoration is a big sign that says "Castle of Elsinore", the characters are going to have to provide a description of the castle in their dialogue if you want the audience to visualize it.
Plus, at the time only the playwrights themselves kept copies of the entire play; the actors were only given their own lines and the cues that came before them. Shakespeare was also rather stingy with stage directions, so the actors themselves needed the lines to know when their characters had died.
In Wicked, Glinda says about Elphaba, after asking if she was born wicked, "She had a father, and she had a mother, as so many do." Less obvious if you take it to mean that she was raised by both parents rather than orphaned, and more interesting once you find out she's a Heroic Bastard; the governor isn't her real father, the Wizard is, but the "as so many do" just takes it into this territory.