My most useful GraphViz hack so far has been a script that reads the schema description out of a PostgreSQL database and turns it into a vaguely Access/SQL Server-like database diagram (a node for each table, arrows representing foreign-key relations).
Someday I'd like to set up a script that takes the query-plan returned by PostgreSQL's EXPLAIN statement and turns it into a diagram with a node for each operation and arrows for dependencies, where the arrow width is proportional to the number of rows involved (again, much like SQL Server's query plan results). This would make it easier to spot the hotspots in a complex plan.
My favourite GraphViz tool would probably be XDot:
http://code.google.com/p/jrfonseca/wiki/XDot
Fast, interactive viewing of GraphViz source files without having to convert them to PNG every time, and can be embedded in your own Python/GTK+ apps.