Matthew Yglesias (now back blogging after some nasty problems with Movable Type) has an interesting series of posts on voting systems.

Current federal law requires the use of single-member districts to elect the House of Representatives (per 2 USC 1 § 2c), but nothing in the constitution requires it—as the Supreme Court noted in Branch v. Smith (538 U. S. ?, 2003). Nor does federal law specify the mechanism for elections, although they must comply with the provisions of the Voting Rights Act of 1965, as interpreted by Thornburg v. Gingles (478 U.S. 30, 1986), and related laws, which may rule out the use of majority-runoff elections in some circumstances.

Ceteris paribus, I’d favor some sort of mixed proportional representation/plurality system for House elections, like the “top-up” PR system used for elections to the Scottish and Welsh assemblies (also known as the Additional Member System); however, the best we can do in the House under current federal law is either approval voting or some other single-member district method (Condorcet or instant run-off being the most likely).