Many of my law school colleagues (especially Judge Richard Posner) were strongly influenced by his work. Foucault's remarks on Becker, noted by Kieran Healy (Sociology, Duke) are quite interesting. In my recent Winter seminar on "Ideology" (with Michael Forster), I assigned sections of Becker's A Treatise on the Family in conjunction with exploring Adorno's idea that under capitalism, society is a "totality," in the sense that (as Brian O'Connor usefully puts it), "Each part of society can be propertly understood only as a part of a whole from which it gains its meaning." Unintentionally, but usefully, Becker makes this point with his analysis of the family under capitalism. Like many important intellectual figures, Becker relentlessly pursued some simple ideas, even to extreme and at times implausible conclusions. I was surprised to learn of his passing, since he was still a frequent presence around campus, and seemed vital and as engaged as ever. I have no doubt the various economics blogs will have better-informed commentary on his work and its import for that discipline.
(Thanks to Rick Hasen and Dean Rowan for the link to Prof. Healey's piece.)
UPDATE: Chicago's memorial notice is informative.