What is the most direct and straightforward, hopefully interactive, method to conduct a For each item Do... loop, where the input list is a selection of polygons?
A word about "interactive". I'm not opposed to a script solution, but it's not the ideal. The basic idea is that the whole process be as dynamic and immediate as possible. Point and click at some stuff, do something with it, point and click at the results, do something else, and so on for an hour or so. Then save the final results and forget about everything in the middle, it was all adhoc and doesn't need to be repeated exactly.
Software at hand is ArcGIS 10 (with 3D and Spatial Analyst), Arcinfo Workstation, and QGIS 1.7 (though don't feel like a solution from a different product is off-topic). In pseudo code the idea is:
for each selected poly in "index_layer" do: clip "raster_layer" by poly geometry to "d:\out\raster_poly[$ID].tif"
In the following image the selected set is outlined in heavy black and with halo text.