James,
I too have had trouble in the past with the Extract by Mask tool. Have you tried using the new Image Analysis window in ArcGIS 10 to extract your new raster? The Image Analysis window is also very handy for setting the output parameters of your new raster. If you are just needing the raster for map-making or temporary purposes, the Image Analysis window is great to use because it does not need to run any geoprocesses. You can select what what layer you would like to mask, the shape of the mask and very quickly it will process a temporary output to use. If you need that new raster for additional analysis, you can then export the raster to a raster dataset.
ArcMap --> Windows --> Image Analysis
Hope this helps!
Best,
Chris B.