Most of the current map APIs quite cleverly use use the build-in vector support in Firefox and Internet Explorer (and others). Firefox supports Scalable Vector Graphics (SVG), while Microsoft use the obsolete Vector Markup Language (VML). The Google Maps API and OpenLayers API automatically check your browser and draws the vectors with the appropriate technology.
But the SVG/VML/DOM technology has some serious performance issues - if you add many complex polygons the browser will run terribly slow. While we wait for HTML 5 (and browsers to support it), Flash APIs might be a better solution.
I recommend Prince McLean's articles about the Flash Wars.
UPDATE 8 JUNE 2008:
Guilhem has made a nice tutorial of how choropleth maps can be created with Google Maps Flash API. He uses the World borders dataset available on this site. The Flash API has currently no way to load geometries from a KML file, so Gulheim manually creates the country polygons through API calls. Try his application and see the benefits of using Flash compared to a SVG/VML/DOM approach an this site (using Google Maps API).