In this paper, we present a study of the scaling properties and intermittency of solar wind MHD turbulence based on the use of wavelet transforms. More specifically, we use the Haar Wavelet transform on simultaneous 3 s resolution particle and magnetic field data from the Wind spacecraft, to investigate anomalous scaling and intermittency effects of both magnetic field and solar wind velocity fluctuations in the inertial range. For this purpose, we calculated spectra, structure functions, and probability distribution functions. We show that this powerful wavelet technique allows for a systematic elimination of intermittency effects on spectra and structure functions and thus for a clear determination of the actual scaling properties in the inertial range. The scaling of the magnetic field and the velocity fluctuations are found to be fundamentally different. Moreover, when the most intermittent structures superposed to the standard fluctuations are removed, simple statistics are recovered. The magnetic field and the velocity fluctuations exhibit a well-defined, although different, monofractal behavior, following a Kolmogorov -5/3 scaling and a Iroshnikov-Kraichnan -3/2 scaling, respectively. The multifractal properties of solar wind turbulence appear to be determined by the presence of those most intermittent structures. Finally, our wavelet technique also allows for a direct and systematic identification of the most active, singular structures responsible for the intermittency in the solar wind.