Good news!  As of February 8th, 2013, we can share documents for viewing and editing via SkyDrive and the viewers/editors no longer need to sign in with a Microsoft Account to view/edit.

Read up on this enhancement on the Inside SkyDrive blog.
Here’s a walkthrough of how easy this is:
  1. To create a new document, log in to your SkyDrive account and use the “Create” menu to create a new document.
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  2. As usual, give the document a meaningful name and click “Create.”
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  3. Add some content to the document that describes its purpose, or you can be as cryptic as possible if you like.  Save your changes.
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  4. From the “File” tab on the ribbon, select “Share,” then select “Share with People.”
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  5. Click “Get a link” and then click the “Create” button under the “View and edit” option.
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  6. The link will be generated for you and you can optionally use the “Shorten” button to get a short URL for the document, which I typically recommend.
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  7. At this point, copy the link to your clipboard, click the “Done” button, and you can email that link to whomever you like.
  8. Anyone who uses that link will be able to view and edit the document and will not be prompted to log in to SkyDrive with a Microsoft Account.
I’m a SkyDrive Insider, ask me about SkyDrive or learn more about the SkyDrive Insiders program here.