I've been reading about using WMS servers to server shapefiles. When a server does support shapefiles over WMS, what format does the client download the shapes in? Will it typically be an image format (png, jpeg, etc) like it is for CADRG, or is there a way to extract the vector data, or will the shapefile data (geometries, etc) typically be part of the metadata available on the server?
Typically an image format. WMS, as an interface, will (for the most part) only provide web-friendly images of your geospatial data (which could be Shapefiles, MapInfo TAB files, GeoTIFF's, etc.). There is simple point-based identify query functionality, which I would say provides limited access to feature data.
If you want to server your Shapefiles and provide access to the geometries/attributes, then check out the Web Feature Service (WFS) specification, which does just this. Here, Geometries/attributes of features are provided using Geography Markup Language (GML) as a baseline, however various WFS implementations offer additional formats.