What would I use Stackless Python for?

It allows you to work with massive amounts of concurrency. Nobody sane would create one hundred thousand system threads, but you can do this using stackless.

This article tests doing just that, creating one hundred thousand tasklets in both Python and Google Go (a new programming language): http://dalkescientific.com/writings/diary/archive/2009/11/15/100000_tasklets.html

Surprisingly, even if Google Go is compiled to native code, and they tout their co-routines implementation, Python still wins.

Stackless would be good for implementing a map/reduce algorithm, where you can have a very large number of reducers depending on your input data.

Stackless Python's main benefit is the support for very lightweight coroutines. CPython doesn't support coroutines natively (although I expect someone to post a generator-based hack in the comments) so Stackless is a clear improvement on CPython when you have a problem that benefits from coroutines.

I think the main area where they excel are when you have many concurrent tasks running within your program. Examples might be game entities that run a looping script for their AI, or a web server that is servicing many clients with pages that are slow to create.

You still have many of the typical problems with concurrency correctness however regarding shared data, but the deterministic task switching makes it easier to write safe code since you know exactly where control will be transferred and therefore know the exact points at which the shared state must be up to date.

Thirler already mentioned that stackless was used in Eve Online. Keep in mind, that:

(..) stackless adds a further twist to this by allowing tasks to be separated into smaller tasks, Tasklets, which can then be split off the main program to execute on their own. This can be used for fire-and-forget tasks, like sending off an email, or dispatching an event, or for IO operations, e.g. sending and receiving network packets. One tasklet waits for a packet from the network while others continue running the game loop.

It is in some ways like threads, but is non-preemptive and explicitly scheduled, so there are fewer issues with synchronization. Also, switching between tasklets is much faster than thread switching, and you can have a huge number of active tasklets whereas the number of threads is severely limited by the computer hardware.

(got this citation from here)

At PyCon 2009 there was given a very interesting talk, describing why and how Stackless is used at CCP Games.

Also, there is a very good introductory material, which describes why stackless is a good solution for Your applications. (it may be somewhat old, but I think that it is worth reading).