\documentclass{article}

 %   \usepackage[english,russian]{babel}
    \usepackage{fontspec}
        %\defaultfontfeatures{Ligatures=TeX}
        %\setmainfont{Cambria}
        %\setsansfont{Calibri}
        %\setmonofont{Courier New}


\begin{document}

1. <<ligatures>> are printed

2. «double quotes» are not printed


\end{document}