We present the first model-independent measurement of the helicity of W bosons produced in top quark decays, based on a 1 fb-1 sample of candidate t events in the dilepton and lepton plus jets channels collected by the D0 detector at the Fermilab Tevatron p Collider. We reconstruct the angle * between the momenta of the down-type fermion and the top quark in the W boson rest frame for each top quark decay. A fit of the resulting cos* distribution finds that the fraction of longitudinal W bosons f0=0.425±0.166(stat)±0.102(syst) and the fraction of right-handed W bosons f+=0.119±0.090(stat)±0.053(syst), which is consistent at the 30% C.L. with the standard model.