How to apply \looseness=-1 to ALL the paragraphs?

At the end? Rather at the beginning. And generally:

\everypar{\looseness=-1}

However it does not mean that every paragraph will be one line shorter.

Dan's suggestion in a comment to Przemysław Scherwentke's answer deserves more visibility:

Finally, one can simply set \linepenalty=1000 (or larger). This adds a penalty for each line and so TeX tries to reduce the number of lines. It is not reset with each paragraph, so it only needs to be set once. Basic LaTeX does not touch \linepenalty except to set the default value (10).