Clipping raster using polyline or polygon using ArcGIS Spatial Analyst?

Use Extract by Mask which:

Extracts the cells of a raster that correspond to the areas defined by a mask.

and specify your polygon feature class of the US as the mask.

With GRASS GIS you could rasterize your polygone of the USA (v.to.rast) and then use a mask.

You can also use the GDAL utility program GDALWarp - http://www.gdal.org/gdalwarp.html

Passing in a -cutline parameter (a feature from any OGR datasource) clips the original raster.

E.g.

C:\gdal\apps\gdalwarp C:\myraster.tif C:\output.tif -cutline C:\inputfeat.json -dstnodata -9999

In GDAL 1.8 there is a new -crop_to_cutline paramter that may also be useful.