I am using sphinx with the pngmath extension to document my code that has a lot of mathematical expressions. Doing that in a *.rst file is working just fine.

a \times b becomes:

However, if I try the same inside a *.py file for example in a module documentation like so:

"""
a \times b
"""

I end up with

Furthermore no amsmath functionality seems to work, either.
What do I need to do, to also have math formulas in my *.py documentations?

Try putting a lower case 'r' before your docstring - like this:

def multiply(a,b):r"""returns a \times b"""return a*b

I've never seen a raw literal string for a docstring before, but this will keep your \t from being interpreted as a <TAB> character.