Let's say you were crazy enough to want to try to combine a number of different technologies just to show that you could do so - what kind of app would lend itself to this type of project as a demo for a potential employer?
Specifically I'm thinking of combining the following technologies:
PHP/Django/Rails/Flex
Does this sound ridiculous or could it be a useful exercise/demonstration of one's abilities?
I dont't think that mixing php, django and rails makes sense for a demo...
I'd mix flex + one of django, php or rails.
You can then use pyamf, for example, so that you flex app can talk to django. Then look up for some php JSON lib and make the same with php + flex with json, and so on...
I think combining PHP and Rails or PHP and Django would make sense, but perhaps not combining Rails and Django. Rails and Django are too similar. They're modern web frameworks based on modern languages. What they lack, compared to PHP, are open source applications.
I suggest combining WordPress or Drupal with Django or Rails. To combine Drupal with Rails, you might try using drupal_fu. You might try a Django site with a WordPress blog nicely integrated, including using Django authentication for comments on the WordPress blog. Or you might do a Drupal site with a custom part of the site written in Rails.
Perhaps one way you could get both Django and Rails into the mix would be to use Rails for the base of your site and use Django as a way to use a Python library (for something that's done better in Python). One example I know of Python being used in a Ruby app is GitHub, which uses Pygments, a library written in Python, for source code highlighting. I don't think they use Django for it, but you could!
Of course, some folks might consider it cliche, but it's also a fairly well-rounded sort of Web project -- there's some database-design in there, some app-dev in your language of choice, some SOA (Web services with SOAP or REST, maybe some RSS as well), some UI design, some UI dev in Flex, and so on.
It's also a familiar-enough idea to the kinds of folks who'll probably be interviewing you, so you won't have to spend lots of time explaining what it is before digging into the technical details, and it's non-trivial, but still something whose scope you can keep under control. I think it's a good project for learning a new Web technology in general.
In terms of which part does what, you might consider doing the CMS with Flex, the majority of the public-facing site with PHP (or Rails) and HTML/CSS, and then adding one or two Flex extras to that as well -- a photo gallery, maybe, or a video/media player. Or what the heck, be different -- just build the whole thing in Flex, like Adobe's done with its XD site.
Have fun and good luck!
If I were an employer, I would be much more impressed if you could implement the same sample application three times:
If you use ReST, then the Flex side wouldn't need to change too much to support each server technology, and you would demonstrate that you're a versatile developer that can learn new technologies quickly.