We use tapered silica fibers to inject laser light into ZnO nanowires with diameters around 250 nm to study their waveguiding properties. We find that high-order waveguide modes are frequently excited and carry significant intensity at the wire surface. Numerical simulations reproduce the experimental observations and indicate a coupling efficiency between silica and ZnO nanowires of 50%. Experimentally, we find an emission angle from the ZnO nanowires of about 90 degrees , which is in agreement with the simulations.