How to remove table in MS Word while retaining the text inside of it

For Word 2010:

• Select the table
• Go to the Tables Tools / Layout tab on the ribbon
• Press Convert to Text

Similar functionality exists in previous versions of Word too.

You could simply cut and paste it into another instance of Word, pasting with "keep text only". Then afterwards you can just cut n' paste back into the original document. Worked for me.