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Is there a way to take a mesh, cut it with seams or sharp edges and flatten it, so that the faces stay the same shape and size?

Making paper models is one aspect, where you could use that technique.

No, I'm afraid SZ0Return is not going to do it properly.

And misusing the UV-unwrap is only a last option.

Note, while it's an option to revert to Blender 2.49 which had a script to do this, I'd like a solution that I can use inside the current workspace.

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    $\begingroup$ Would be great if someone could update the 2.49 script, it was quite advanced. $\endgroup$ – ideasman42 Jun 3 '15 at 23:23
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There is an exporter for paper models, it even has a Blender Wiki Page with in depth usage guidelines.

For more information and plenty of examples of successful use cases you can read the BlenderArtists thread by the developer of the script.

Add seams like you would for any regular texturing job, experiment with simple geometry first. Here is an icosphere.

enter image description here

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    $\begingroup$ That's an awesome addon. Nice find. $\endgroup$ – wchargin Aug 12 '13 at 21:45
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    $\begingroup$ Agreed, the developer seems very eager to attack any bugs that lurk within. $\endgroup$ – zeffii Aug 12 '13 at 21:49
  • $\begingroup$ I really want to use this addon as well, but the download button takes me to a wall of text... how am I supposed to download that? $\endgroup$ – Espen Sales Apr 9 '17 at 21:22
  • $\begingroup$ Espen, search for how to install add-ons $\endgroup$ – zeffii Apr 10 '17 at 18:08
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For Blender 2.8+ the paper model addon is available at GitHub

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