We report on the experimental demonstration and analysis of a new waveguide principle using subwavelength gratings. Unlike other periodic waveguides such as line-defects in a 2D photonic crystal lattice, a subwavelength grating waveguide confines the light as a conventional index-guided structure and does not exhibit optically resonant behaviour. Subwavelength grating waveguides in silicon-on-insulator are fabricated with a single etch step and allow for flexible control of the effective refractive index of the waveguide core simply by lithographic patterning. Experimental measurements indicate a propagation loss as low as 2.1 dB/cm for subwavelength grating waveguides with negligible polarization and wavelength dependent loss, which compares favourably to conventional microphotonic silicon waveguides. The measured group index is nearly constant n(g) ~1.5 over a wavelength range exceeding the telecom C-band.