Pictured: Your great-grandchildren?
As a redheaded science journalist, I hear this "fact" a lot. Reality is, though, we aren't going anywhere. Yes, as Cara Santa Maria points out at Huffington Post, redheads represent only about 1% of the world's population. And this hair color is related to a recessive gene. Both your parents have to have a copy in order for you to be a redhead, so a redheaded person can have non-redheaded babies. But that's not the same thing as going extinct. Because here's our little secret: We redheads are stealthily infiltrating the rest of humanity. Only 1% of humans are redheads, but 4% of humans carry a copy of the gene that makes redheads. You could be a carrier and not even know it. So could your spouse. Two redheads are unlikely to make a brunette, but two brunettes can make a redhead. Good luck wiping us out. *Insert evil laughter here*
You can learn more about this at Cara Santa Maria's Talk Nerdy To Me vidcast, but I'll add a little piece of anecdata, too. My parents are both brunettes. So were their parents. I am largely an anomaly on both sides of my family. In fact, besides my brother and I, the only other redhead in my Mom's entire family (that anyone remembers) was her grandfather. And yet still, we rise.
How Stuff Works also has a great debunking of the redhead extinction myth
Some more info on how redheads are in yer genome, gingerin' yer descendants from the Stanford University Tech Museum
Image: Four shades of Red, part II, a Creative Commons Attribution Share-Alike (2.0) image from e3000's photostream