The wave equation explains why some sounds are pleasing to our ears and why some just makes us grit our teeth (nails down the chalk board, anyone?). It is also modified in studying earthquakes to let us understand the phenomenon and predict little stuff like tsunamis.
Maxwell's equations are the base of our communication technology: from the old telegraph to our mobile phones. Schrodinger's cat may or may not be in the box (or both dead AND alive), but his equation translates quantum mechanics into things like your DVD player and smart phones. As for Fourier transform, suffice to say that you can thank him for removing unwanted noise from your recording and the manipulations to make your digital photographs prettier.
Equations make the world go round.
Vive le numbers!
*All stolen from newscientist.com.