In no particular order:
Enforce property rights
This includes enforcing contracts, protecting personal property, etc.
Protect the commons
If there are problems of externalities, the government should step in. The environment, for example. We all suffer when the environment declines but we're not the people screwing it up. Make sure that mining operations set aside enough for clean up. Make sure that lumber operations preserve the forests. Make sure that farming doesn't create some monocultural wasteland.
Build infrastructure
Protecting the commons is about preventing destruction of common resources. Building infrastructure is the logical counterpart. Where everybody benefits but nobody can afford it, the government should build it. This includes roads, water services, public transportation, IT infrastructure, etc. How to determine what fits as a positive ROI investment is up for debate.
Break down agency problems
Make sure that people who can reap the benefits of risk-taking are subject to the negative repercussions. Never let individuals or institutions take risks that they can't absorb themselves. Make sure that people pay for the wrongs they commit and try to make sure they benefit from the good they do.
Stay out of people's personal lives
The government has no business mandating private issues when they are kept private. "Private" means that people who don't like what is happening aren't subjected to it against their will. Religious observation is naturally private. Sexual orientation is private. Marriage, the arts, parenting style, recreational activities, etc. are all private as long as the participants are all consenting (and legally able to consent).