One option:
If you're using Word 2003 and the email addresses are formatted as
hyperlinks - and there are no other hyperlinks - go to Edit>Find. Do not
type anything into the "Find what:" field. Put a check in the "Highlight all
items found in:" box (make sure it's set for Main Document), then click the
MORE button. Open the Format list & choose Style, then select Hyperlink from
the Style list. After clicking Find All, close the Find dialog box, copy the
selected hyperlinks, then paste into a new blank doc. You should get a list
of the email addresses when you paste.
If you're using Word 2007 the process is almost the same. The Find feature
is located on the HOME tab, and instead of a Find All button you click the
"Find In:" button & choose Main Document there. When you do, all hyperlinks
in the doc will be selected. Also, once you close the box & copy/paste the
links they get pasted into the other doc as plain text rather than live
hyperlinks. If you want them as active links you can use the Format Painter
in the original doc to copy the Hyperlink formatting, then select all the
links in the new doc to format them - or you can just select them in the new
doc & apply the Hyperlink style.