My primary language right now is D, and I'm in the process of learning Python because it's required for a course I'm taking.  While I understand why dynamic languages would be a breath of fresh air for people programming in static languages without type inference or templates (IMHO templates are to a large extent compile-time duck typing), I'm curious what the benefits are of dynamic languages even when you have those.  
The bottom line is that, if I'm going to learn Python, I want to learn it in a way that really changes my thinking about programming, rather than just writing D in Python.  I have not used dynamic languages since I was a fairly novice programmer and unable to appreciate the flexibility they supposedly offer, and want to learn to take full advantage of them now.  What can be done easily/elegantly in a dynamically typed, interpreted language that's awkward or impossible in a static language, even with templates, polymorphism, static type inference, and maybe runtime reflection?
In theory, there's nothing that dynamic languages can do and static languages can't. Smart people put a lot of work into making very good dynamic languages, leading to a perception at the moment that dynamic languages are ahead while static ones need to catch up.
In time, this will swing the other way. Already various static languages have:

Generics, which make static types less stupid by letting it select the right type when objects are passed around, saving the programmer from having to cast it themselves
Type inference, which saves having to waste time on writing the stuff that should be obvious
Closures, which among many other things help to separate mechanism from intention, letting you pull together complicated algorithms from mostly existing ingredients.
Implicit conversions, which lets you simulate "monkey patching" without the risks it usually involves.
Code loading and easy programmatic access to the compiler, so users and third parties can script your program. Use with caution!
Syntaxes that are more conducive to the creation of Domain Specific Languages within them.

...and no doubt more to come. The dynamic movement has spawned some interesting developments in static language design, and we all benefit from the competition. I only hope more of these features make it to the mainstream.
There's one place where I don't see the dominant dynamic language being replaced, and that's Javascript in the browser. There's just too much of an existing market to replace, so the emphasis seems to be towards making Javascript itself better instead.
Uses for Dynamic Languages