Kelsey Gramar shaved off Frasiers beard when he started "FRASIER" because they didn't think John Mahoney would be believable as his father.

Tom Bosley shaved off his big sideburns when he began playing his role of Howard Cunningham on Happy Days.

The rest of these are sort of iffy, so please correct as necessary:

Bob Denver had shaved off the goatee he had sported on The Many Loves of Dobie Gillis (until 1963) by the time he became the star of Gilligan's Island (1964-up).

John Astin I don't believe ever appeared with a moustache prior to The Addams Family as Gomez Addams.

Rob Reiner may have grown a moustache to appear as Mike Stivic on
All in the Family -- I can't recall if he had one when guesting on
The Partridge Family.

I think Christopher Hewett might have done that for Mr. Belvedere.

When he was guest-starring on the 1984 E/R, which was shortly-after Fantasy Island, he was still clean-shaven.

But when he did the pilot for Mr. Belvedere shortly thereafter, it was the first time he was seen with a mustache. He may have been required to grow one for the show. Regardless, he kept it until his death in 2001.

richard moll shaved his head to play the role of bull on night court

David Carradine shaved his head to play Caine on Kung Fu -- and I think several other actors as well, like Keye Luke (Master Po).

Jackie Coogan shaved his head so he could play Uncle fester on The Addams Family.

Jonathon Frakes grew a beard in the hiatus between season 1 and season 2 of Star Trek The Next Generation. The producers liked it and so Commander Riker had a beard for the rest of the series.

I see someone beat me to mentioning Jonathan Frakes as Commander Riker on "Star Trek: The Next Generation". I don't know that his beard was really required per se for the show, but yeah- it's definitely different watching him in Season 1 and then seeing the bearded look in the rest of the series- the beard is the iconic look now.:) :cool:
And speaking of iconic beards, I have to mention Michael Gross as Steven Keaton on "Family Ties". I remember a long while back first seeing some Season 1 episodes and for a second not recognizing who was playing the father- before I figured out that it was just Steven without a beard. And yeah- it definitely looks quite different and from Season 2 to the end of the series, Steven has a beard. I don't know that the show necessarily required it, but my understanding is that they liked it and wanted him to keep it- and yeah, his beard is iconic too.

You forgot Kim Cattrall. in the final season of Sex and the City, Samantha found out she had breast cancer and lost her hair to chemo. Kim obliged by shaving her hair. It was so romantic when Smith shaved his hair short to match his girlfriend's head. Katherine Heigl shaved hers on Greys Anatomy

Right before Howie Mandel started his syndicated talk show in 1998, The Howie Mandel Show, he had facial hair -- but shaved it off just prior to the series' beginning. There's no question it was done for the show, because he also ditched his earrings at the same time (later to return).

I heard that for the Ironside reunion movie, done shortly before his death in 1993, Raymond Burr not only trimmed his beard to a smaller goatee but he also dyed his hair a brown-reddish color in order for viewers not to be confused with his Perry Mason role on the return movies of the time (by then Burr himself had white-gray hair and near full-beard).

Avery Brooks, who played Hawk on Spenser: For Hire and on its spinoff A Man Called Hawk shaved his head, even though he still had a fairly full head of hair before that.

Smallville: Michael Rosenbaum shaved his head for the role of Lex Luthor. Also, in one of the seasons, the character of Lionel Luthor has all of his long hair dramatically buzzed off on-screen.

David Hyde Pierce had a beard for a few eps on Frasier but then shaved it off. They wrote that change in very nicely with a really sweet scene between Niles and Daphne on why "Island Niles" disappeared so quickly.

John Stamos' haircut was addressed on Full House in "Cutting It Close". I'm not sure if the haircut was intentional and then written as an ep, but that's one of my favorites.

Jackie Coogan shaved his head so he could play Uncle fester on The Addams Family.

Coogan also shaved off his mustache for the role.

Avery Brooks, who played Hawk on Spenser: For Hire and on its spinoff A Man Called Hawk shaved his head, even though he still had a fairly full head of hair before that.

And he started DS9 clean shaven with a full head of hair, but after a few years it was his head shaven and his face goateed.

The late Pernell Roberts not only began sporting gray-whitish facial hair when he signed on to do Traper John, M.D. but in-between the long gap after he left Bonanza and way before Trapper John, M.D. started, he also ditched his hairpiece as well, especially noticeable during his guest star appearance on a Season 3 episode of Hawaii Five-O.