Recs.
Updated
Built by the company JetBrains who are pretty well known for their IntelliJ IDEA product that works with Java and the JVM in all its forms.
SpecsUpdate
Pros
Pro Great for navigating large codebases
PyCharm has amazing code navigation implementations. It supports both goto symbol and goto declaration. The former finds classes, variables, functions, etc by name. While the latter is used by moving the cursor on top of a symbol and by using the mouse or a keyboard combination it finds the declaration of that symbol and takes you there.
Both of these features are extremely helpful when consulting large code-bases and when trying to understand an API written by someone else.
Pro Free student access to Professional Edition
With a valid .edu address students can register to use the Professional edition and enjoy all the perks of the full paid version for free.
Though it should be mentioned that the with the free student acess you cannot use PyCharm for any commercial purposes, even accepting donations for an open source project.
Pro Vim mode for people used to Vim commands
IdeaVim supports motion keys, insert mode commands, marks, registers, visual mode commands, vim regexps, key mapping, macros, digraphs, some ex and :set commands. You can find a full comparison in the IdeaVim reference manual.