Socially responsible investing has come a long way since the 1960s, when the civil-rights movement spurred some investors to try to match their investments with their values. Now, it's commonly known as environmental, social and governance investing, or ESG, reflecting three prominent areas of concern for socially conscious investors.

This type of strategy has long been associated with institutional investors like college endowments and pension funds, but there's also a wide variety of mutual funds available for individual...