Code-completing/auto-completing ArcPy scripts using Notepad++ (external editor)?

PyScripter is my choice. It's free and open source and a lightweight and quick install. There is even a registry-free installation that doesn't require admin rights for installation.

I recommend WingWare IDE. It seems to have the best debugging and code completion out of the Python IDEs I've seen. One of the motivating factors for arcpy in 10.0 was that it would have better code completion than arcgisscripting offered.

MS recently released Python Tools for Visual Studio - once you follow a few steps outlined here: http://blog.guerrillagis.net/?p=878 Visual Studio will provide you with intellisense, method signatures, syntax highlighting, a REPL and a debugger.