Tools for analyzing C++ codebase

Which tools would be most useful for analyzing a C++ codebase? What do they cost?
Can we manage with free and trial software, or are there commercial software that is good and that we really should to pay for?

The main object would be to get an understanding of quality - memory issues etc, also to understand the code (For spotting architectural problems for example), perhaps coding standards.

Primarily statical analysis, but we are hoping to be able to run the code. Think it needs to be "robust in the sense that it should work with code for arcane compilers.