I have also used FLIP, SELECT CASES and a back-FLIP to get rid of empty variables
in a dataset:

* Example dataset with 6 variables & several missing data *.
DATA LIST LIST/var1 TO var6.
BEGIN DATA
1.0     7.5     -999    -999    -999    -999
1.0     6.2     -999    -999    -999    4
1.0     6.9     -999    -999    -999    -999
1.0     7.4     -999    -999    -999    -999
1.0     9.2     -999    -999    -999    -999
1.0     8.3     1       -999    -999    -999
1.0     7.6     -999    -999    -999    -999
2.0     5.8     -999    -999    -999    -999
2.0     7.3     -999    -999    -999    -999
2.0     8.2     -999    -999    -999    -999
2.0     7.1     -999    -999    -999    -999
2.0     7.8     -999    -999    -999    -999
2.0     7.2     -999    -999    -999    2
2.0     7.3     -999    -999    -999    -999
3.0     5.9     -999    -999    -999    -999
3.0     6.2     -999    -999    -999    -999
3.0     5.8     -999    -999    -999    -999
3.0     4.7     -999    -999    -999    -999
3.0     7.3     5       -999    -999    -999
3.0     7.2     -999    -999    -999    -999
3.0     6.2     -999    -999    -999    -999
4.0     6.2     -999    -999    -999    -999
4.0     6.8     -999    -999    -999    -999
4.0     5.7     -999    -999    -999    -999
4.0     4.9     -999    -999    -999    7
4.0     6.2     -999    -999    -999    -999
4.0     5.8     -999    -999    -999    -999
4.0     5.4     -999    -999    -999    -999
END DATA.
RECODE var3 var4 var5 var6  (-999=SYSMIS)  .
EXECUTE .
* All cases for var4 & var5 are sysmiss *.
LIST.

STRING newvar(A8).
COMPUTE newvar=CONCAT('f',LTRIM(STRING($CASENUM,F7))).
PRESERVE.
SET ERRORS=NONE RESULTS=NONE.
FLIP /NEWNAME=newvar.
* The following lines were contributed by someone at the list, they
  simplified my original code *.
COMPUTE xxx=$SYSMIS.
COMPUTE ncases = NVALID(f1 TO xxx) .
* End of added lines *.
SELEC IF ncases NE 0.
MATCH FILES FILE=* /DROP=ncases xxx.
FLIP /NEWNAME=CASE_LBL .
MATCH FILES FILE=*
/DROP=CASE_LBL.
EXEC.
RESTORE.
LIST.