Thank you for the nice response,
I kmow that in practice transposing the matrix is a common, but do not think
of it as a very valid approach. (Higher order) Factor analysis with oblique rotation 
and restrictions penalizing nonzero loadings would sound good for me. Would
you know of any references for such an approach?

  In SPSS all of the few dozen Proximity (similarity measures) can be applied to variables.  (After the data are transformed and transposed)  The  Proximity matrix can then be read into the variety of cluster procedures.  Or the transposed data can be read directly into the CLUSTER, or Quick cluster procedure.  I see no reason (given that you want to cluster variables) that the TWOSTEP cluster could not read a transposed data matrix.

  Of course there are all of the varieties of factor analysis which are more commonly used to group variables.  The CATPCA procedure factors categorical variables.

  When the variables are used to classify or differentiate a categorical variable, there are procedures like DISCRIMINANT  or the various