[jcranmer]

The problems most people have with static typing are related to explicit typing, not static typing per se. (And somewhat inane conversions tend to give dynamic typing a bad name as well).

There are two cases I can think of where the static typing in the most common languages are insufficient. The first is union types--you can't easily express a data structure like JSON in Java (although one could argue this is a feature, not a bug). The second case is where you need to map types to instances of those types, something akin to a Map<Class<T>, T> in Java syntax. While you can generally specify the latter at a method syntax (e.g., public <T> T get(Class<T> clazz)), there's no way to write that method without having to resort to subverting the type system.

Dynamic typing can be beneficial if you would otherwise be stuck subverting the type system more often than following it, although that's as much of an argument for more powerful static type system as it is one for dynamic typing.