Sam,
Not natively, but you could convert your text column to a table using
Table - convert - convert text to table - choose paragraph as the list
separator - OK. This should give you a one column table. Then copy the one
column into your other table, providing you have a simple structure (no
merged cells and such) this should work.
Luc

Hi Sam,

This worked when I tried it, but I'm not sure it's a general
solution...

First select your column of text, go to Table > Convert > Text To
Table. Make sure it says it's going to create 1 column and as many
rows as there are paragraph marks in your selection, and click OK.
That makes a table. Drag the right border to make it narrower. Select
the whole table and copy it to the clipboard.

Now go to the other document. Click the ¶ button so you can see
nonprinting characters, including the table's end-of-cell and
end-of-row marks. Put the cursor after the last character in the top
right corner of the existing table. Tap the right arrow key once,
which puts the cursor between the table border and the first
end-of-row mark. Paste from the clipboard -- you should get a new
column to the right of the existing table.

If you want the new column somewhere in the middle instead of the
rightmost, select the column and drag it to where you want it.

--
Regards,
Jay Freedman
Microsoft Word MVP         FAQ: http://word.mvps.org