The Chicago Plan, which was the idea of a group of University of Chicago economists in the 1930s, was that bank deposits be 100% backed by reserves i.e., government-issued money. This 'narrow banking' proposal would separate the money and credit functions of banking, and mean that all money in an economy would be government-issued money. A recent IMF working paper has argued that such a system would eliminate bank runs, give governments better control of the business cycle, and dramatically reduce public and private debt. Click here for Daily Telegraph comment on this working paper. There is a group in the UK called Positive Money who are campaigning for narrow banking.
From my perspective, the Chicago Plan would mean that banks are risking investor and not depositor money whenever they make a loan. However, the main problem with the Chicago Plan is that near-bank institutions issuing near-money would spring up and circumvent the 100% reserve requirement.