It is demonstrated theoretically and experimentally that the low energy density of states N(E) is described by a singular V-shape form N(E)=N(0)(H)+alpha|E|+O(E2) for all clean superconductors in a vortex state, irrespective of the underlying gap structure. The linear term alpha|E| which has not been recognized so far is obtained by exactly evaluating the vortex contribution. Based on microscopic Eilenberger theory N(E) is evaluated for the isotropic gap, line, and point-node gaps to yield a V-shape N(E). Scanning tunneling spectroscopy-STM experiments on NbSe2 and YNi2B2C give direct evidence for this. We provide arguments on the significance of this finding and on the relevance to other experiments.