Is there any API or web service to create statistical world maps where the values are different shades of a colour?
Google Charts has an API just for that. There's a 'map' type of chart
You will need to pass in at least 2 params.
CHD = that's your values for say "population" - 100, 300, 700, whatever. And
CHO = That's your start and end color values (say red and green) and the API will do the rest.
In the link above, search for "This map demonstrates using color gradients." and you'll see a basic example.
Any basic GIS software will do the trick if you have the proper geographic layers.