I have a worksheet of contact data that is in columns for convenience
in editing, but needs to be in rows in order to be used by Word as a
mail merge data source.

I used TRANSPOSE (the function, not the Paste Special option) to
populate a worksheet with transposed values, but all the blank cells
from the original (where a contact does not have, for example, a fax
number, etc.) are populated with zeros. ...

When I use the transposed sheet as a data source for Word mail merge,
all these zeros come in. ...

Is there anything I can add to the TRANSPOSE function applied to the
cells in the target worksheet to get rid of these zero values?

The following doesn't use the TRANSPOSE function, but maybe it'll help.

If the original data is in Sheet1, put this in Sheet2!A1
=IF(OFFSET(Sheet1!$A$1,COLUMN()-1,ROW()-1)="","",
OFFSET(Sheet1!$A$1,COLUMN()-1,ROW()-1))
Then extend the formula to the right and down as far as needed.

I have Office 2003 for Windows.