Most obviously, if you want to run one of Oracle's layered applications (e.g supply chain management or whatever). Sure you probably could beat it into running on Postgres but why would you?

Oracle (the database) is meant to be the integration point for Oracle (everything else). If you aren't running any of Oracle's other products, then it boils down to a pure technical decision - do you need feature X? Is it cheaper to buy it or build it? For example do you use OpenFiler or buy VVM or use ASM that comes with Oracle since you need a database anyway? Or maybe you have exotic spatial data needs. Or you want virtual private database/label security (http://wiki.postgresql.org/wiki/RLS - Oracle has had this for years, the Postgres guys are still talking about it, the MySQL camp don't even know that there is such a thing).

Now, I am a long-time Oracle user, and even I say, unless you know and can say specifically why you need Oracle, then you should use Postgres or SAP/DB (or in place of Oracle XE, maybe even SQLite). But if you do need it, then it's Oracle or DB/2, choose your poison.

Well, despite some promising open-source efforts in the area (PostGIS being most prominent) Oracle is still tops when it comes to handling geo-spatial data. Unfortunate, but that's the way it is.