I need to take a region of spreadsheet cells and paste them into a Writer document as a table.
How do I do this?
Select and copy the cells from Calc.
The Paste Special dialog will appear.
Select HTML (HyperText Markup Language) and click OK.
Your copied cells will now be pasted into the document as an HTML table.
For all intents and purposes this is now a table in Writer and not the embedded object you would have seen from a simple copy-paste.
A quick Google search brings up this thread: http://www.oooforum.org/forum/viewtopic.phtml?t=44629
You can already paste as a new table, apparently. But to paste into an existing table, you need to first paste into a new document, then copy that and then paste it into the original table using the "Paste Special > HTML" command.
To elaborate on @8Days' answer:
You must Paste Special into the top-level of the document. It does not work properly if you are creating a table inside a table cell (Writer gets confused), and you have to first paste special into the top-level of the document, then you can cut+paste into a table inside a table cell.