Think of your favorite novelists, poets, actors, directors, singers, and so forth. Which of them (if any) was most active and renowned before your birth? If the answer is none, is there any particular reason?
Elvis was still alive when I was born in 1968, but he was at his hottest before that. I wish I could have gotten with that and I’m not sure I’ll ever get over it.
I’m happy to add “before you were old enough to really appreciate them” to the “before you were born” criterion.
Vera Ellen.Of her movies, I’ve only ever seen White Christmas, and boy, is that good for me.
Okay, yes, that would be good. It would be better if you could bring back Hottie Elvis from the 50’s just for one night and steer him in the direction of my house.
There were many, many, many groups from the late 50’s that I love. That was ten years before my birth. Joan Baez, Everly brothers and Aretha Franklin are three that come to mind.
Probably the biggest genius was Hank Williams. That guy was doing stuff that wasn’t repeated in country music for another thirty years. He was way ahead of the times.
[evil skald]
Wait … do you want a time-displaced Elvis from 1959, or a hookerbot that looks, sounds, smells, etc. exactly like him but is pronounced to service your whims? 'Cause Rhymer Industries can handle either one, but it’s two separate departments.
[/evil skald]
Billie Holiday. Not really knowing what she was all about, I bought a cassette of some of her old stuff just to hear “Gloomy Sunday”, the famous suicide song, and ended up practically wearing out the cassette. It went from there to buying everything of her’s I could find. And she’s good at lullabying me to sleep. 
One of my favorite science-fiction authors was H. Beam Piper. He died(as in committed suicide) about the time I was in kindergarten. God, I love his work, I have copies of everything I know about that he wrote.
Any of the blues legends. I saw a few in the very early 80’s (Muddy, the Hook, Gatemouth, Willie Dixon, etc) but that was after their heyday and the Howlin’ Wolf was long gone by the time I learned what the blues were, nevermind Robert Johnson, et al.
REM’s heyday, the 80s IRS years, was before I was born.
Ben Webster, Louis Armstrong, Cole Porter, Duke Ellington, Clifford Brown: all great jazz artists
Anita Baker, Ella, Billie, Edith Piaf
Humphrey Bogart, Judy Holliday (watch Born Yesterday to see the greatest ditsy blonde role ever played), Cagney for the most part
H. Ryder Haggard, the author of such classics as Alan Quatermain (the model for Indiana Jones), She, King Solomon’s Mines, and more.
Edgar Allan Poe and H.G. Wells; Robert Service.
I’m a big fan of First World War poets Siegfried Sassoon and Wilfred Owen, who both meet your criteria.
Jane Austen died a bit before I was born, too.
It’s a cruel trick of fate that I missed New York in the 70s, including Warhol’s Factory, Max’s Kansas City, the Soho art scene (Gordon Matta-Clark, Laurie Anderson, many others) and Studio 54.
And CBGB. Especially CBGB. Blondie, Talking Heads, Ramones, Patti Smith… I was lucky enough to see Debbie Harry and the Dictators perform on the eve of its closure in 2006, but I felt out of place as a child of the 80s and 90s.
When I read the thread title I thought of literally artists, you know with paint, and thinking about it now that’s probably the only kind that applies for me anyway. I love N.C. Wyeth.
I believe I’ve mentioned my fondness for Louis Armstrong and the Andrews Sisters here before. Satchmo died before I was born, as did LaVerne, and I was an infant when the surviving Sisters made their last comeback.
I would love to see the Rolling Stones between 1968 and 1972 when they really were the world’s greatest rock 'n roll band.
I’m a huge fan of classic movies, but being born in 1980, I naturally missed the heyday of all of them. Liz Taylor, Cary Grant etc
I have no idea if all those classic movies were loved as much in the 40s/50s/60s as they are now. Did they people back then realize how great those actors were? Did people say “OMG another Jimmy Stewart movie, we have to go see it!!!1!” OTOH, back in the day, you had a lot more unique actors then you do now since the whole movie thing was a lot newer, there just weren’t as many leading men.
In other words, we look back at classic movies as a heyday, but I wonder if they knew it was a heyday. I wonder if they knew it was something special.
For music, as much as I love my classic rock (again, before my time), if I had to pick one group it would probably be The Supremes. I remember even as a little kid, seeing them on TV and having my jaw drop. I was just utterly amazed by them.
I love art nouveau, especially work by Alphonse Mucha.
Too many authors to mention all of them. Orwell, Solzhenitsyn, Dostoevsky, Vonnegut (who did publish quite a bit during my lifetime, but whose heyday was before me), etc.
In comic books, Sheldon Mayer, writer/artist of Sugar and Spike, which ended three years before I was born. Comic strips, Charles Schulz; my favorite Peanuts strips are from 1950-1970.
Not too much in music; my favorite genres tend to be newer. The “oldest” bands I love would be Sonic Youth and Siouxsie and the Banshees, both of whom started when I was a kid. I love pop music and electronic dance music, but they generally age pretty badly, so I tend to listen mostly to stuff in these genres from within the last few years. There are plenty of artists I like from before I was born, but “love” is a bit strong.
Movie directors: Kubrick (both before and during my lifetime), Welles, Murnau, Lang, Pabst, Chaplin.