From what I have seen and read on blogs, PyPy is a very ambitious project. What are some advantages it will bring to the table over its siblings (CPython, Jython, and IronPython)? Is it speed, cross-platform compatibility (including mobile platforms), the ability to use c-extensions without the GIL, or is this more of a technical exercise on what can be done?
PyPy is really two projects:

An interpreter compiler toolchain allowing you to write interpreters in RPython (a static subset of Python) and have cross-platform interpreters compiled standalone, for the JVM, for .NET (etc)
An implementation of Python in RPython

These two projects allow for many things.

Maintaining Python in Python is much easier than maintaining it in C
From a single codebase you can generate Python interpreters that run on the JVM, .NET and standalone - rather than having multiple slightly incompatible implementations
Part of the compiler toolchain includes an experimental JIT generator (now in its fifth incarnation and starting to work really well) - the goal is for a JITed PyPy to run much faster than CPython
It is much easier to experiment with fundamental language features - like removing the GIL, better garbage collection, integrating stackless and so on

So there are really a lot of reasons for PyPy to be exciting, and it is finally starting to live up to all its promises.
What does PyPy have to offer over CPython, Jython, and IronPython?