Ah, but since I never watched Moonlighting he was new to me.
Yeah, I know I’m grasping at straws. 
I remember Rachel Leigh Cook as the your brain on drugs girl.
I remember Katherine Heigl as the teen daughter in My Father the Hero, but I don’t think that counts since that was basically her breakout role. I add it anyway because you could argue that was her child-star career breakout role, and her grown-up career is a separate thing altogether. (I remember her grown-up career starting with Valentine only because I didn’t see 100 Girls until years later on cable.)
That really doesn’t count, though. That’s like saying you remember Keira Knightley from Pirates of the Caribbean.
Dazed and Confused is in the running:
Adam Goldberg
Matthew McConaughey
Cole Hauser
Milla Jovovich
Joey Lauren Adams
Ben Affleck
Parker Posey
Nicky Katt
When I was a kid I watched a lot of old 50s B-grade horror flicks on TV. I remember thinking that the lab technician in “Revenge Of The Creature” and the fighter pilot in “Tarantula” looked mighty familiar. It was a very young Clint Eastwood.
Pierce Brosnan in The Long Good Friday.
He looks about 15.
When I saw her in Big Trouble in Little China, I remembered her as the chick who screamed like a murder victim when she got banged by the Gym teacher in Porky’s, from a few years before Police Academy. I loved that scene…
Joe
Yeah, It seemed like every time I saw a movie for the next three years after I saw that, I was saying, “Waitaminit, wasn’t he/she in Dazed and Confused?” Amazing. And it happened again when I saw “Rent,” with Anthony Rapp. Apparently, he was also in “A Beautiful Mind,” which I saw before Rent, but didn’t notice him in it.
ETA: According to IMDB, he was in “Twister” as well. Missed him in that one, too. I wonder why I recognized him in Rent, but not those…
Joe
WheresGeorge04, Anthony Rapp was in “Adventures in Babysitting” well before Twister or Rent. (I think his teenage boy character in “Adventures in Babysitting” has a lower voice than Mark in “Rent.”)
And before “Dazed and Confused!” I saw “Babysitting” in the theater too, but didn’t recognize him in “Dazed.”
Joe
I believe Jennifer Aniston played his sister on the short-lived Ferris Bueller TV show. That was pretty awful iirc.
Jim Carrey on The Duck Factory, anybody?
I clearly remember recognizing Alanis Morrisette, after her album came out, as the wee little girl on You Can’t Do That On Television
How about the movie Colors? It had Don Cheadle as Rocket, Gerardo (of “Rico Suave” fame, who was also in “Can’t Buy Me Love” with Patrick Dempsey) as some Hispanic gangster, AND a very young (looked to be about 13 or 14) Mario Lopez who appeared with no lines walking in a crowd of people for a couple scenes.
My sister was visiting me from college for a week in the mid-'80s and every day she watched soap operas and for that week so did i. i don’t remember which one it was, but on one soap there was this young actress so beguiling (to me at least) i told my sister i’d have to keep watching the show just to see her. (didn’t, natch!)
years later talking about Forrest Gump, my sister told me “Jenny was so-and-so on some-soap that you said was so hot.”
Crazy about Robin Wright right off.
Speaking of Viggo, he was in one of the Texas Chainsaw Massacre sequels. I can’t remember if he was in the one with Renee Zelwinger(sp?) or if that was Matthew McConahay(sp?) in the one she was in.
Dana Plato was in a Nat Geo Mag Ad around ‘75…forgot what she was sellin’, only that she was in a chair in a bedroom with a “DANA” t-shirt on, the letters were them cheesy iron-on ones.
Dang she was cute.
Why do I remember?..I dunno,
Other than that musta’ been a pretty interesting issue.
There wasn’t too much internet, gaming or cable TV then.
Also an alumnus of Hill Street Blues, in which he played the leader of the Shamrocks, IIRC at an early point in the series.
I remember the show, and a couple familiar cast members, but it was a while after Carrey started getting famous that I made the connection.
I’ve been watching reruns of The Rockford Files and saw James Cromwell in a very small part. Looked him up on IMDb, it was his first credited role.
In a special on Tiger Woods, they showed an appearance he made on The Mike Douglas show when he was three.
I remember seeing it when it first aired.
This does not count, since I only learned it recently, but we watched The Treasure of the Sierra Madre (1948) again last night (I’d seen it before, first time for the wife), and the little Mexican boy selling lottery tickets is Robert Blake! Read that in Leonard Maltin and looked it up on Imdb, and it’s him. Sure does not look like him.
George Clooney in the sitcom E/R has been mentioned. But I also remember Jason Alexander from that show. He played Mr. Stickley, a hospital administrator.