The problem isn't usually suppressing the field, but ensuring that the blank
space you need when the field has something in it is not there when the
field is empty.

e.g. suppose you have

{ MERGEFIELD firstname } { MERGEFIELD middlename } { MERGEFIELD lastname }

If firstname is Peter and lastname is Jamieson, but middlename is blank, you
will get

Peter  Jamieson

(i.e. with two spaces between the names).

To suppress that you can for example
a. use the \b switch in the MERGEFIELD field in Word 2002 and later to
insert the necessary spaces, e.g.

{ MERGEFIELD firstname }{ MERGEFIELD middlename \b " " }{ MERGEFIELD
lastname \b " " }

b. use nested IF fields, e.g.

{ MERGEFIELD firstname
}{ IF "{ MERGEFIELD middlename }" = "" "" " { MERGEFIELD middlename }"
}{ IF "{ MERGEFIELD lastname }" = "" "" " { MERGEFIELD lastname }" }

c. create an Access query that returns exactly the string you want,
typically using iif functions to insert additional space when the related
field is non-blank, then use that as the data source for the merge. If you
are more familiar with the Access query language than the Word field
language, there's a lot to be said for constructing the entire address that
way.

NB, all the {} need to be the special field codes you can insert using
ctrl-F9, not the ordinary keyboard characters.

Peter Jamieson