Does Inkscape have a 'save selection" command?

No, it hasn't.
It doesn't seem to make sense to save a selection in a vector graphics program. That command is common in bitmap edition programs, where a selection creates a channel that affects several pixels and it's really hard to re-create the same selection twice.

For me it makes sense in two scenarios:
  1- you create graphics to be included in a LaTeX document

  2- as above, but you also use an inkscape document as a repository of "most common graphics" (in my case electronic symbols like gates, flip-flops and the like)

For the first case now I'm doing:

  1- open a blank document whose page size is that of the maximum area figures can fill in a LaTeX page, this way, if the graphic fits inside the Inkscape document it will not fill the margins in the LaTeX document

  2- draw it

  3- select all items

  4- fit page to selection (to adjust the abuttment box for PDFLaTeX)

  5- save document as PDF (later it will be loaded by PDFLaTeX)

  6- undo the 'fit page to selection'. If you do not do this, next time you edit the graphic you will not have the size reference, so you will not know if the edited graphic fits inside the LaTeX patch

  7- save the document as SVG for future editing

With a "save selection as" command the process will be:

  1- open a blank document whose size is that of the maximum area figures can fill in a LaTeX page

  2- draw it

  3- select all items

  4- save selection as PDF (later it will be loaded by LaTeX)

  5- save the document as SVG

You need neither the fit page to selection nor undo commands. Not a big problem not having the save selection, but read below...

  In the second scenario you have a "mother" template document containing your "library" of graphics. These graphics, in fact, are all outside the document page limits, the part of the document inside its page limits being blank. Then the process is:
  1- open a new document with this template

  2- copy/paste some of the "library" graphics (laying outside page limits) to build your new graphic (inside limits). As in the previous case, page limits are the same size as the LaTeX patch)

  3- when done, select only your new graphic

  4- save the just created graphic (using the save selection) in PDF format (for LaTeX and with the proper abuttment box)

  5- then save the whole doc as SVG for future editing. In the future you still have all "library" graphics inside the inkscape document

 I have found this approach to be much faster that having a library of symbols on disk or using two documents (one the graphic, the other the library) simultaneously with the clipboard. Of course uses more disk, but this is not an issue for me. Unfortunately not having the "save selection as" (almost) invalidates this approach. This is the reason I asked for the save salection function. I said "almost" because replacing step 4 in the previous process by:

  - invert selection

  - delete

  - select all

  - fit page to selection

  - save as (PDF)

  - undo

  - undo

  You can do the same thing, but it is much more cumbersome.

  I'm a new user to Inkscape, so perhaps it has some other tools, unknown to me, that can help me doing this kind of things, but I honestly think that this function will heavily speed up the workflow.

  Regards.

Thanks Guillermo, but your solution still does not solve my problem. When new-file, paste, save I still need to fit page to selection ... if I want the correct abuttment box in the final graphic.

I think I will mark this problem closed and file a feature request.

Regards.

Thanks Guillermo Espertino (Gez), that solved my question.