For many nonvolatile memories, - including flash memories, phase-change memories, etc., - maximizing the storage capacity is a key challenge. The existing method is to use multilevel cells (MLC) of more and more levels. The number of levels supported by MLC is seriously constrained by the worst-case performance of cell-programming noise and cell heterogeneity. In this paper, we present variable-level cells (VLC), a new scheme for maximum storage capacity. It adaptively chooses the number of levels and the placement of the levels based on the actual programming performance. We derive its storage capacity, and present an optimal data representation scheme. We also study rewriting schemes for VLC, and present inner and outer bounds to its capacity region.