The following websites provide interactive maps that can be exported or screengrabbed as static images (jpgs) or other formats, but not as vector illustrations. They also all provide data table downloads that can be joined to census shapefiles.
Social Explorer (library subscription)
The online program Social Explorer is the simplest method for creating a map of Census data. This program contains Census data from 1790 to the present, offers a fast and effective way to map data, and even allows for the simple creation of time-lapse slideshows of demographic variables. Social Explorer is available in both a free basic version, as well as a premium version available through U-M Libraries. See their help section for guides on creating maps.
American Factfinder (free and public)
American Factfinder has excellent mapping capabilities. The site can sometimes be slow or buggy, so be patient. You can control classification (breaks), colors, and transparency of the main variable you are mapping. You can also control what other information appears on the map, including adding labels, boundaries, and text callouts. Output options are varied, though no vector graphics output is available.
SimplyAnalytics (library subscription)
For more complex maps, try using Simply Analytics, available through U-M Libraries. If you wish to save your work on Simply Analytics, it is necessary to create a log-in. Once on the website there are various Help topics and tutorial videos to assist you in creating your map.