I use Photoshop to design interfaces and then cut down the graphics, by using the rectangular marquee tool and selecting the area that I want to save, copy-merged and then paste into a new document, of the correct canvas size according to the selection area, and then save for web..
This is horrendous.
I end up with dozens of open windows all "Untitled" something, unsaved.
All I want is being able to select an area in my document using the marquee tool and then select from File a save function like "Save selection for web and devices...".
Perhapse this option could be in the "Save for web and devices.." dialog, where you could select from a dropdown the following:
"Entire document" (default)
"The entire selected area"
"Trimmed down selected area"
Slices may help. Have you read the documentation for Slices and tried that?
Could you use this sequence - perhaps as an action - to create a duplicate image, crop duplicate to suit, save, then discard the duplicate:
Image > Duplicate
Marquee tool (make desired selection rectangle)
Image > Crop
Save for Web
Edit > Close (click No to "Save changes to ... copy before closing")