Use a conditional field
{IF{Mergefield fieldname} <> 0 "{Mergefield Fieldname}"}
See also http://www.gmayor.com/formatting_word_fields.htm

Hi Nasscott,

To fix this:
. press Alt-F9 in your mailmerge document to toggle the field code display
on. You should see something like:
{Mergefield DataField} or {Mergefield DataField \# 0.00}
.edit the field code so that it formats the result how you want it. For
example:
{Mergefield DataField \# $,0.00;($,0.00);}
will show the value as dollars and cents, with -ve values in brackets, and
the final ';' suppresses 0 output.

If you're working with what is meant to be purely textual data, formatting
the field as {Mergefield DataField \# ;} will likewise suppress any 0s
(along with any other mixed alpha-numeric output).

If you need to show mixed alpha-numeric output, but suppress errant 0s, try:
{IF{Mergefield DataField}= 0 "" {Mergefield DataField}}
to do this, you'll need to:
. copy & paste your mergefield, so that you get
{Mergefield DataField} {Mergefield DataField}
.select both mergefields and press Ctrl-F9 (to wrap them in another field,
thus-
{{Mergefield DataField} {Mergefield DataField}}
. fill in around the field braces as indicated, taking special care with
spacing.

Cheers