We have studied the microstructure, surface states, valence fluctuations, magnetic properties, and exchange bias effect in MnO2 nanowires. High purity alpha-MnO2 rectangular nanowires were synthesized by a facile hydrothermal method with microwave-assisted procedures. The microstructure analysis indicates that the nanowires grow in the [0 0 1] direction with the (2 1 0) plane as the surface. Mn3+ and Mn2+ ions are not found in the system by X-ray photoelectron spectroscopy. The effective magnetic moment of the manganese ions fits in with the theoretical and experimental values of Mn4+ very well. The uncoupled spins in 3d(3) orbitals of the Mn4+ ions in MnO6 octahedra on the rough surface are responsible for the net magnetic moment. Spin glass behavior is observed through magnetic measurements. Furthermore, the exchange bias effect is observed for the first time in pure alpha-MnO2 phase due to the coupling of the surface spin glass with the antiferromagnetic alpha-MnO2 matrix. These alpha-MnO2 nanowires, with a spin-glass-like behavior and with an exchange bias effect excited by the uncoupled surface spins, should therefore inspire further study concerning the origin, theory, and applicability of surface structure induced magnetism in nanostructures.