Unfortunately, unlike Crystal Reports (please see tip above), SSRS does not have a ninja 'suppress blank fields' option, so you have to write a formula to accomplish this.
Here is a sample formula to use if you want to have the Customer Name (CUSTNAME), Customer Number (CUSTNMBR), 3 address lines (ADDRESS1, ADDRESS2, ADDRESS3), city (CITY), state (STATE) and zip code (ZIP) in one field with the empty fields suppressed:
=First(Fields!CUSTNAME.Value, "DataSet1") + " - "
+ First(Fields!CUSTNMBR.Value, "DataSet1") + VbCrLf
+ iif(First(Fields!ADDRESS1.Value, "DataSet1") = "", "", First(Fields!ADDRESS1.Value, "DataSet1") + VbCrLf)
+ iif(First(Fields!ADDRESS2.Value, "DataSet1") = "", "", First(Fields!ADDRESS2.Value, "DataSet1") + VbCrLf)
+ iif(First(Fields!ADDRESS3.Value, "DataSet1") = "", "", First(Fields!ADDRESS3.Value, "DataSet1") + VbCrLf)
+ First(Fields!CITY.Value, "DataSet1")
+ ", " + First(Fields!STATE.Value, "DataSet1")
+ " " + First(Fields!ZIP.Value, "DataSet1")