Done in an old Chuck E. Cheese commercial. The voiceover says, "Boring restaurants make you wait...and wait...and wait," while time lapses are shown with a kid sitting at a table waiting, ending with cobwebs and a ridiculously long beard. This is contrasted with the kid excitedly playing games at Chuck E Cheese.
Fist of the North Star: Not only does Kenshiro grow a beard in the animated movie in between his assault by Shin and encountering Bat and Lin (And then shaves it using some thug's knife), but he also develops a beard at the start of the second series, shaving it once he finally begins to fight again.
Done in Thorgal - after he escapes from caves where time flow was slowed, he wakes up with a long beard the next day. Not at all played for comedy, as the girl he was with had spent most of her life there and got aged into a shrivelled husk overnight.
Superman in the Time And Time Again story arc in 1991 gets a Time Passage Beard as he is stuck in the prehistoric past with no way of getting home except to expose himself to explosions and powerful energy discharges.
In The Kingdom of Gods, Sieh keeps magically aging whenever he uses too much of his power or does anything particularly unchildlike, such as remembering he's a father. Each time this happens, he ends up with a massive beard and head of hair.
Crichton does this a few times in Farscape, notably while he's stranded on an alien planet in "Jeremiah Crichton".
In the sixth series of Doctor Who, the opening two-parter has the Doctor (who had always been beardless previously) imprisoned for several months and growing a beard. It happens again in the season finale.
Also from the revived Doctor Who; in "The Doctor's Wife", Amy stumbles across Rory's dead body in a Room Full of Crazy, having grown a beard, aged, and eventually starved to death. Don't worry, he gets better.
House the season 2 finale has House awaken from a coma. He determines roughly how long he had been out (three days) by the amount of growth of his Perma Stubble.
Chief O'Brien grows one in the virtual prison cell that he spends twenty virtual years in in an episode of Star Trek: Deep Space Nine.
In How I Met Your Mother, Ted becomes part of a very long discussion about Teddy Roosevelt with another man and a woman. He explains it went of for "days" and by the end, the other man and Ted have grown long beards.
In one scene in the "Blood Gulch Chronicles" of Red vs. Blue, Church spends a thousand years standing in a hallway waiting for a computer to fabricate a teleporter (...maybe). By the end of it, Church has a massive beard drawn on his sprite. Played for laughs, given he's in a robotic body at this point.
Parodied in an episode of Tiny Toons where Babs is looking for a personal hero in old cartoons. As she sits in the Acme Looniversity archive the camera pans around and when it comes back to her she has a long gray beard and a cane. She tosses the cane aside, then rips the beard off and is about to storm off in frustration but decides to watch one more film.
Averted in The Smurfs episode "Smurf Van Winkle" (and its comic book counterpart "The Strange Awakening Of Lazy Smurf"), where the only characters seen with any Time Passage Beards are the Smurfs that claim that Lazy has slept for a few hundred years. Of course, the whole thing was a Faked Rip Van Winkle, since the Smurfs were wearing fake beards.