Make a Map is a website that lets you create your own maps of the US and areas thereof using various demographics data. It’s still in beta stage but it’s got all of the US and so far has datasets for median household income, population change 2000-9, population density, median home value, unemployment rate, average household size and median age. The sitemaker, ESRI (Environmental Systems Research Institute, Inc.), also has a pretty good free globe map software, ArcGIS Explorer, for which you download map layers and add-ins. ArcGIS has been used for several years now by the U.S. Census.
Other (non-ESRI) mapping alternatives:
GeoCommons | MapBox | Geoda | QGIS | Maps Geek | Tableau Public | Polymaps | Needle | Leaflet
10 Free Tools For Creating Your Own Maps
To help students get started, here is a list of research-quality data sets: