My list starts with:

-fund basic research in science and engineering -fund nascent beneficial commercial efforts where private interests fear to tread - supply infrastructure and services that are useful to most but are natural monopolies are network effects monopolies. (i.e. roads, rail,air, healthcare, research labs, weather services to name a few) - punishing cheating. i.e. fraud, externalities such as pollution, shifting costs onto the public to enhance profitability, and all forms of financial engineering. - protection against catastrophic loss - protection of vulnerable people - limiting corporations and individuals from gaining society distorting power.