Banking is a very vast domain. The classic approach is that there is a central
integrated financial/customer based engine (usually called core) surrounded by
dozens of outer systems such as front-end, back-end, GL, card/switch, reporting,
T/F, etc.

So the question is whether you want to know about core or the rest of the world?

As much as I know, Java is not the dominant solution in core but its quite apt
among surrounding systems. This atmosphere against using Java as the main
computational engine is changing gradually (not only in banking, also in other
critical systems) but still you may find oldish alternatives such as CICS,
Tuxedo and NetWeaver just kicking. So, in the case that using Java itself is a
big question mark, let alone Hibernate and Seam ;)