I'm hoping to write an expanded post about this, but for now: we're using the 2009-2013 American Community Survey (a product the Census Bureau puts out yearly, rather than the every-ten-years Census). You can download CSVs of the whole thing here: http://www2.census.gov/programs-surveys/acs/summary_file/201.... We took those and TIGER data (geospatial data specifying what areas each of the stats in the CSV correspond to), and put them into a Postgres db with PostGIS.

If you're not looking to show the whole US at a granular level like we are, you might be able to skip the FTP server approach a few ways. They recently released CitySDK (https://uscensusbureau.github.io/citysdk/), which seems like a nice way to get at Census data from the browser, though I haven't personally used it. There's also a set of APIs (https://www.census.gov/data/developers/data-sets.html), which might work depending on what specifically you're trying to do. A third way to get at it is to use American FactFinder (http://factfinder.census.gov/faces/nav/jsf/pages/index.xhtml), which lets you drill in and search for whatever fields and/or geographies you care about, and export them.

If you just want to browse around Census data, I also love Census Reporter (http://censusreporter.org).