In one episode of Mr. Bean, the title character got locked out of his hotel room naked, and is forced to navigate the building wearing signs. Amusingly, the sign he wears over his genitals reads "Private" and the sign over his bottom reads "Exit". In the same episode, he loses those signs later, only to replace them with "Out of Order" and "No Entry" respectively. And beforehand, he covered his front with a fire extinguisher.
A very early episode has Hawkeye bet Trapper that he could walk stark naked into the mess tent and everyone in camp would be too bored to notice. Hawkeye manages to cross the compound wearing only a hat and boots via a creative camera setup with soldiers carrying long planks between Alda and the camera. Once in the mess tent he manages to stand in line and get some food before someone notices and drops their tray. He then backs out using an army tray to cover himself.
Trapper(laughing) Pay up! 50 bucks!
Hawkeye(covering himself with the tray) You'll have to wait, I left my pockets in the Swamp.
Once, Hawkeye manages to get B.J. good: Beej wakes up in the nurses' tent, surrounded by women, and completely naked in bed; he tries to grab the sheets, but they're nailed in place. Finally, he gets a pillow and covers his more interesting bits with it, then backs out of the tent... to a full waiting audience.
Another episode has Margaret stealing Hawkeye and B.J.'s clothes while they are in the shower. They have to leave the shower tent with "Their heads held high, and their hands held low".
One of the film's most famous scenes was of a showering Hot Lips doing this when Hawkeye and Trapper exposed her in full view of the entire base. Without that bit of history, the TV series simply painted Burns and Houlihan as intolerant. Which they were, but in the film their bitterness was somewhat justified.
In The Young Ones, Neil runs into the room wearing a T-shirt and holding a strategically placed flowerpot to angrily confront the others. It escalates until he is about to hit Rik with a kettle held in both hands overhead, when Rik says, "Neil! How are you keeping that flower pot up??" He drops the kettle, grabs the pot and flees for the stairs.
Chris in Skins does the hand variant when he gets locked out of his own house naked.
J.D. is caught doing the naked chicken dance by Dr. Cox. Instinctively, he grabs the nearest object he can reach to cover up his privates — which unfortunately turns out to be a picture of Cox's son. Given Cox's (understandable) anger, J.D. switches it with a different picture... that turns out to be of Dr. Cox.
A subversion occurs in another episode with the guest-character Molly Clock; she covers her breasts with her arms even though she's wearing clothes, because she wants the men to whom she's talking to pay attention to her words, not her body.
The Naked Trucker And T Bones Show would serve as one of the best examples of this, were it still around. A fine case of Exactly What It Says on the Tin, it's a show about two guys, T-Bones (played by David Koechner) and the nameless Naked Trucker (played by the incomparable Dave "Gruber" Allen, everyone's favorite guidance counselor). Naked Trucker is never seen wearing more than a baseball cap, boots, and a guitar.
On NCIS, a stray iguana startles Tony awake, and Gibbs and Kate come running, guns drawn, at his startled outcry. As soon as they realize it's not a threat, the others turn to Tony (who'd been sleeping in the buff), and he grabs a chair to invoke this trope.
Angel: In the episode I Will Remember You, during his day as a human, Angel uses a tub of ice-cream to hide his groin as he's returning to bed with Buffy.
And later, in "Life Of The Party", he does it with a pillow.
Buffy the Vampire Slayer. Spoofed in "Go Fish" when Xander struts into the pool area having secretly joined the swim team, only to be confronted by the female Scoobies staring at him in surprise and some rather frank appreciation. Even though he's already wearing speedoes, a suddenly embarrassed Xander grabs a float board and a tube of lotion to cover the same region.
In, "Nightmares", Xander finds himself in class in his boxers. His response to that is to cover his chest.
Highlander pulled a pillow version with Duncan in one episode as well. Only it was apparently not his doing, a female immortal bounty hunter had him tied to the bed.
One later episode of Red Dwarf has Lister and Rimmer being marched into see the captain after getting accidentally infected with nano-tech that disintegrates their clothes and hair. They use both hands to cover themselves as they are marched once again down that long corridor.
A Halloween episode of Psych, with David Naughten as guest star, paid homage to the above scene in An American Werewolf in London by having Sean and Gus find a self-proclaimed werewolf in their garage, wearing nothing but a bunch of balloons.
In Merlin, Arthur walks out from behind a modesty screen in the buff, only to be confronted by Guinevere who has rushed into his chambers to rescue him from a Brainwashed and Crazy Merlin (long story). Arthur grabs a pillow to cover himself as Guinevere tries to explain herself. What makes the scene is that Gaius, the elderly court physician is also present, trying to hide Merlin behind a curtain and clearly struggling not to laugh.
Hustle: Danny Blue loses a game of Strip Poker and attempts to salvage what is left of his dignity with a strategically placed cushion.
Three's Company had an episode where they played strip poker, ending with a "winner take all" hand. As they left Furly's apartment (where the game was held), Larry was covering himself with a newspaper, the two girls he brought with him had Modesty Towels, Jack was wearing a box and Furly had two pillows.
MuchMusic in Canada once had "Not Much On Day", which featured host Rachel Perry hosting nude while covering herself with her arms, sitting down with her legs in front of her as well as various objects, including newspapers, lights, trophies, Censor Boxes, balloons and melons.
Rizzoli & Isles: In "Class Action Satisfaction", Jane and Maura have to take a decontamination shower after being exposed to a potential pathogen. After coming out of the shower, Jane tries to keep a medical waste bin between her and anyone else.