The Living Wage Calculator defines a living wage as "hourly rate that an individual must earn to support their family, if they are the sole provider and are working full-time (2080 hours per year)."
It is sometimes tied to the official poverty line for a family of four. Which for the U.S. in 2013 is $23,550 or $11.25/hr.
Congressional Research Service report Fair Labor Standards Act: Overview (June 4, 2013) - gives overview on the legal status of workers and wages. No mention of "living wages" in this annual review although earlier ones did, but good focus on minimu wages and exemptions.
Minimum Wages by David Neumark and William L. Waschler. Cambridge: MIT Press, 2008) - a e-book by former MSU MSU Economics Professor now at University of California Irvine and Director of the Center for Economic Research and Policy.
Economic Policy Institute - has among one of its foci Wages, Incomes, and Wealth and has done studies on the effectiveness of living wage ordinances.
Employment Policies Institute - is a non-profit research organization dedicated to studying public policy issues surrounding employment growth.
National Employment Law Project - resources on laws and reports and links to other resources.
Partnership for Working Families - Policies and tools from a national network of leading regional advocacy organizations who support innovative solutions to our nation’s economic and environmental problems.
Political Economy Research Institute - has a page focused on Labor, Wages, and Poverty that includes research on 'living wage" ordinances.
University of California, Berkeley Labor Center - has a page with reports and links to additional resources.