<p>Right now I'm developing mostly in C/C++, but I wrote some small utilities in Python to automatize some tasks and I really love it as language (especially the productivity). </p>

<p>Except for the performances (a problem that could be sometimes solved thanks to the ease of interfacing Python with C modules), do you think it is proper for production use in the development of stand-alone complex applications (think for example to a word processor or a graphic tool)?</p>

<p>What IDE would you suggest? The IDLE provided with Python is not enough even for small projects in my opinion.</p>

In my opinion python is more than ready for developing complex applications. I see pythons strength more on the server side than writing graphical clients. But have a look at
http://www.resolversystems.com/
. They develop a whole spreadsheet in python using the .net ironpython port.
If you are familiar with eclipse have a look at
pydev
which provides auto-completion and debugging support for python with all the other eclipse goodies like svn support. The guy developing it has just been bought by
aptana
, so this will be solid choice for the future.
@Marcin
Cons: as a dynamic language, has way
  worse IDE support (proper syntax
  completion requires static typing,
  whether explicit in Java or inferred
  in SML),
You are right, that static analysis may not provide full syntax completion for dynamic languages, but I thing pydev gets the job done very well. Further more I have a different development style when programming python. I have always an ipython session open and with one F5 I do not only get the perfect completion from ipython, but object introspection and manipulation as well.
But if you want to write second Google
  or Yahoo, you will be much better with
  C# or Java.
Google just rewrote jaiku
to work on top of App Engine, all in python. And as far as I know they use a lot of python inside google too.