Beardness Protection Program

A man who is on the run or otherwise trying not to be recognized will often grow a beard as part of his attempt at concealment. The inversion -- where a heavily bearded character shaves for similar reasons -- is also relatively common, doubling as an Important Haircut.

A sufficiently Crazy Prepared character might grow a beard so that, sometime in the future, he'll be able to shave it off and go unrecognized - maybe this is the reason for the Beard of Evil?

If the character in hiding is ashamed of what he's done, it may also count as a Beard of Sorrow.

Wig, Dress, Accent is another variation on the theme.

Comic Books

 * In recent years, Bruce Banner has tried once shaving his head, and another time growing a beard to disguise himself from the authorities pursuing him. Consequently, we got to see a bald Hulk and a fuzzy-faced Hulk.
 * Shows up briefly in the Spirou and Fantasio album "Machine qui rêve". The comic opens with a bearded man pursued by the authorities, who shaves his beard off in a bar's bathroom because his image is being broadcast on the news channels.

Film -- Live Action

 * In the film version of The Fugitive, the second thing Dr. Kimble does after escaping from prison is shave off his beard. (The first thing is to ditch his orange jumpsuit.) That is, Harrison Ford begins the film with a beard only to lose it after 20 minutes and look like himself for the rest of the film.
 * Inverted in an early draft of the script, where Kimble grows a beard in order to disguise himself.
 * In the 2002 film of The Count of Monte Cristo, the Count does this, trimming his scraggly Beard of Sorrow into a refined nobleman's beard to pose as the Count. It even fools his love interest for a bit.
 * It helps that everyone thinks he's dead (or close enough to it).
 * Following: When "Bill" fears that a witness would be able to connect him to a robbery, he then gets a haircut and shaves his beard.
 * In Don't look now... We're being shot at!, Sir Reginald shaves his iconic "Big Mustache" because it looks too British and would make him stand out.
 * In the first Highlander movie, the Kurgan does a very messy job of shaving his head hair to evade police capture after several witnesses see him lop off a guy's head.

Literature

 * In the Lord Peter Wimsey book The Nine Tailors, Nobby Cranton grows a beard before going to look for a diamond necklace he'd stolen some decades before.
 * As does Lord Peter himself, when infiltrating a criminal gang in one of the short stories.
 * In The World According to Garp by John Irving, a paedophile molests a girl in the park, then shaves off his moustache in a public toilet to avoid the police.
 * In A Song of Ice and Fire:
 * Jaime keeps the beard he acquired in captivity, then shaves his head for good measure. It doesn't seem to fool anyone.
 * There's also Ser Barristan Selmy, who grows a beard sometime between
 * In the Worldwar (Literature) series, Moishe shaves for the first time in two decades as part of his escape from a ghetto.
 * The James Bond novel Moonraker has an example of the prepared-in-advance version.
 * Garion suggests this to Zakath when he joins them in the Malloreon. Zakath has no trouble complying, because he doesn't know how to shave. Garion's a little incredulous that a man at his level of power/paranoia would let other people near him with a straight razor.
 * Doubly inverted in The Prisoner of Zenda -- in order to impersonate the king, the protagonist shaves off his beard. (Both he and the king are bearded, but he uses the shave to explain "his" change of appearance.)
 * In Neil Gaiman's Stardust, Primus shaves his beard. He doesn't expect to fool his rival, but simply to have an extra moment to react before he was recognized. Its effectiveness is never tested.
 * Attempted by Buck Williams in the first Left Behind novel, and is lampshaded by his boss Steve Plank, who comments how unnecessary he believes it to be.
 * Romance of the Three Kingdoms records Cao Cao's rout by Ma Chao's forces, where they first target "the one dressed in red" - so he loses his red robe. Then they target "the one with the beard", and so he shaves his beard. And then they start looking for "that guy with the shaved beard"...
 * In Going Postal, Reacher Gilt has an elaborate beard as part of his pirate "look". He shaves it when he has to go on the run after his plans fail. Since he was planning on disappearing if his plans succeeded (before people started asking for their money back), he seems to have had this in mind from the start.
 * Early in High Deryni, Morgan and Duncan are depicted sporting beards and wearing the colours of the rebel leader Warin deGrey while gathering intelligence, partly among Morgan's own subjects. When they report to Kelson, the king comments on the fact he's never seen them with beards before, and Duncan notes how effective their disguise has been.
 * In the Dutch childrens book Het geheim van Mories Besjoer (The secret or Maurice Bonjour) a French resistance fighter grows a big mustache and uses Monsieur Moustache as his alias, planning to shave himself clean if he ever had to flee from the Germans.

Live Action TV

 * Duncan grows a beard like this near the end of the first season of Veronica Mars. Unless it's a Beard of Sorrow; at the time that he grows it, he's both depressed and running away from home.
 * In the pilot of White Collar, Neal grows a beard in prison, and then shaves it off the day he escapes so he won't be recognized. He doesn't look all that different, but he does look just different enough to fool the facial recognition on the prison security cameras.
 * In Law and Order Criminal Intent, a criminal had a thick beard but had it shaved once he got in the country.
 * In Breakout Kings the team figures that a big prison break was supposed to have another participant who missed the escape because he was sent to the prison infirmary. He stands out since he recently shaved his head so he would look different from his mugshot pictures.
 * George Bluth of Arrested Development briefly has a beard after becoming a fugitive, though he shaves it as soon as he starts hiding out in the model home's attic.

Video Games

 * Team Fortress 2: The Spy has a miscellaneous item called a "Camera Beard" that's equal parts this trope and Shoe Phone.
 * In Arcanum, the "Gnome" you met at the start of the game is quickly revealed to have been a Dwarf, who shaved his beard (inconceivable to their culture) to flee from something.

Webcomics

 * In The Adventures of Dr. McNinja, a variation on the idea of growing a beard just to be able to shave it off for an easy disguise is the reason the McNinja family all wear ninja facemasks at all time. If no-one knows what they look like, then when they really need to, they'll be able to take their mask off and disappear.

Western Animation

 * In Santa Claus Is Comin' to Town, this is supposedly why Kris Kringle first grows his beard. His wanted posters had him beardless and he wasn't an iconic toy-making symbol just yet. The bearded form is, according to the special, the symbol it is because he grew the beard to escape the law.

Real Life

 * Saddam Hussein, who grew a very large beard when he went into hiding from the U.S. army.
 * Radovan Karadžić
 * Vladimir Lenin, plus a wig.
 * Che Guevara
 * Charles Darwin. After publishing 'On the Origin of Species' he became very famous, but he wanted no part of the controversy that followed. So, to go about unrecognized, he grew his now iconic long, woolly beard. It worked so well that even his close friends didn't recognize him at scientific conferences. Ironically, the modern world wouldn't recognize him without the beard.
 * French General Henri Giraud shaved his mustache just before his escape from a German POW camp in World War II.