Currently, there appears to be no federal or state law expressly prohibiting this practice. The ACLU and others argue that this practice violates a candidate's right to privacy. Others are taking the issue a step further and proposing legislation to prohibit this practice, including the Illinois General Assembly. That legislation, HB 3782, would prohibit public employers from seeking job applicants' social media passwords. The proposed legislation would allow candidates to file lawsuits if they are asked for access to sites like Facebook. Employers could still ask for usernames to view public information.
UPDATE: 3/30/2012: On 3/29/12, the Illinois House passed the legislation by a vote of 78-30.
UPDATE: 8/1/2012: Governor Quinn signed the legislation, which will become effective January 1, 2012.