Coupling between subwavelength-diameter silica wires and silicon-based waveguides is studied using the parallel three-dimensional (3D) finite-different time-domain method. Conventional butt-coupling to a silica-substrated silicon wire waveguide gives above 40% transmission at the wavelength range from 1300 to 1750 nm with good robustness against axial misalignments. Slow light can be generated by counter-directional coupling between a silica wire and a two-dimensional (2D) silicon photonic crystal slab waveguide. Through dispersion-band engineering, 82% transmission is achieved over a coupling distance of 50 lattice constants. The group velocity is estimated as 1/35 of the light speed in vacuum.