On a related note, the Rabin-Miller primality test is needed just to find the primes for RSA to work.
I'd consider DH slightly more important.
I think it would be hard to argue that any other single modern algorithm had as much effect on the world as RSA.
MP3?
Discrete cosine transform and its variants gave us jpeg and mp3
Oh, you're absolutely right of course. I completely overlooked that. In that case, I think that the top two prizes should go to one Fourier transform related algorithm and one algorithm from public-key cryptography.