If you have an active selection, Color to Alpha will only affect the selected parts of the image. Thus, you just need to select the background (e.g. with the Magic Wand tool) and then apply Color to Alpha, leaving the un-selected areas untouched:
(Original image by Creative Tools, used under the CC-By-SA 2.0 license.)
See Making the background of an image transparent in Gimp for a more detailed step-by-step explanation, from which the sample images above are taken.
(Of course, if you don't wish to preserve any shadows or reflections in the background, then you can simply Cut it away instead, as jsbueno suggests in his answer.)
There are several variations on this technique that will let you fine-tune the selection afterwards. One is to make two copies of the layer you're editing, convert the selection to a layer mask on the upper copy, and apply Color to Alpha to the (entire) lower copy. This way, you can edit the mask to fine-tune the border between the opaque and semitransparent parts of the image.
Alternatively, you can create a pure white layer (with an alpha channel) under the layer you're editing, cut out the selection from this white layer, and again apply Color to Alpha to the entire image layer. Again, by painting and/or erasing the white layer, you can adjust which parts of the image should be opaque. One potential advantage of this method, if you intend to place the resulting shape over a specific background, is that you can also paint other colors onto the lower layer to help it blend with the new background.