Where do companies like Google and Yahoo and Mapquest get their street and road data? Is this a data source that the public has access to?
Google Maps and MapQuest have gathered data and information through subcontractors and their own internal efforts. Their information is proprietary and is very hard to gain access to (and most methods of scraping this data would violate their Terms of Service). It's generally not considered a reliable source for getting anything beyond geocoded addresses.
An alternative method for getting more specific geographic data (e.g. building footprints, forest extents, roads/highways, POIs, etc.) is through the OpenStreetMap Project. This information is Open and crowd-sourced with very few limitations. Specific information can be grabbed through their Overpass API or can be downloaded as a whole in their pbf format which can then be converted to shapefile/GML.