Because of the decentralized nature of US elections it's difficult to find a free, public source for county or precinct level election data. The Federal Election Commission only publishes state-level results. The Census Bureau does not publish data on election results - they publish survey data from the CPS that shows how many people are registered and how many voted - but not who they voted for.
The National Atlas (which no longer exists - de-funded) did publish county-level results. Previously, if you searched http://www.data.gov/ for Presidential General Election Results county you'd find archived versions of the data from 2012, 2008, and 2004. But - in 2017 this data mysteriously vanished from the repository. Luckily I had saved copies of them, and you can access them from my college's repository here:
There's also a project at Harvard where they're gathering county and precinct data, but the county results appear to be state by state: http://projects.iq.harvard.edu/eda/pages/about.
Gathering it the hard way would be to go to each election office, state by state... the Harvard site has a link to each state secretary of state who is charged with collecting this information - Wikipedia also provides direct links back to individual state election results pages.