We investigate electromagnetic scattering from nanoscale wires and reveal the emergence of a family of exotic resonances for source waves close to grazing incidence. These grazing resonances have a much higher Q-bandwidth product and thus, a much higher Q factor and broader bandwidth than the pure plasmonic resonances found in metal nanowires. Furthermore, these grazing resonances are much less susceptible to material losses than surface plasmon resonances. Contrary to the process of exciting surface plasmon resonances, these grazing resonances can arise in both dielectric and metallic nanowires and appear near to the cutoff wavelength of the circular waveguide. This peculiar resonance effect originates from the excitation of long range guided surface waves through the interplay of coherently scattered continuum modes coupled with first-order azimuthal propagating modes of the cylindrical nanowire. These first-order cyclic Sommerfeld waves and associated cyclic Sommerfeld resonances revealed here opens up the possibility of an alternative scheme of enhanced fields with a better merit (higher Q-bandwidth product and lower loss) than conventional surface plasmon resonances in the nano-regime. This nanowire resonance phenomenon can be utilized in broad scientific areas, including: metamaterial designs, nanophotonic integration, nanoantennas, and nanosensors.