The quantum ferromagnetic transition of itinerant electrons is considered. It is shown that the Landau-Ginzburg-Wilson theory described by Hertz and others breaks down due to a singular coupling between fluctuations of the conserved order parameter. This coupling induces an effective long-range interaction between the spins of the form 1/r2d-1. It leads to unusual scaling behavior at the quantum critical point in 1 < d ≤ 3 dimensions, which is determined exactly.