Which Python IDE can run my script line-by-line?

If you like R's layout. I highly recommend trying out Spyder. If you are using windows, try out Python(x,y). It is a package with a few different editors and a lot of common extra modules like scipy and numpy.

It's not an IDE, but you can use pdb to debug and step through your Python code. I know Emacs has built in support for it, but not so much about other editors (or IDEs) that will run in Windows.

The only one I've had success with is Eclipse with Pydev