There's an externally maintained list of IDEs that's pretty comprehensive at http://wiki.python.org/moin/IntegratedDevelopmentEnvironments. We'll cover some basics and some favorites here. One of the main install/configuration issues with using an IDE is specifying the version of Python. This usually isn't difficult, but can be confusing to a new user. This is especially important to do if you wish to write Python code that works with ArcGIS, each version of which comes with a particular version of Python. For your code to successfully manipulate your instance of ArcGIS, it needs to run using the ArcGIS version of Python. Most of the time, developers use their IDE to run their Python scripts. Therefore the IDE needs to know which version of Python to use (i.e., you probably can't just use the default version that came with the IDE).