Global register allocation is one of the most important optimizations in a compiler. Since the early 80s, register allocation by graph coloring has been the dominant approach. The traditional formulation of graph-coloring register allocation implicitly assumes a single bank of non-overlapping general-purpose registers and does not handle irregular architectural features like overlapping register pairs, special purpose registers, and multiple register banks. We present a generalization of graph-coloring register allocation that can handle all such irregularities. The algorithm is parameterized on a formal target description, allowing fully automatic retargeting. We report on experiments conducted with a prototype implementation in a framework based on a commercial compiler.