Using XeLaTeX the following document produces the correct result if \setmainfont{Arial} is never called (the quotation marks are proper left- and right-quotation marks). Once I try to set a font (even if it has the proper glyphs!) the output appears improperly as ``Quote me!''.
\documentclass{article}
\usepackage{fontspec}
\setmainfont{Arial}
\begin{document}
``Quote me!''
\end{document}


Ligatures=TeXfeature for the font:\setmainfont[Ligatures=TeX]{Arial}– Gonzalo Medina Feb 06 '14 at 18:34! Package xkeyval Error: 'TeX' undefined in families 'Ligatures'.– aardvarkk Feb 06 '14 at 18:38texlive. Should be up to date. – aardvarkk Feb 06 '14 at 20:47fontspecdocumentation, I found thatLigatures=TeXseems to be associated with LuaTeX? Instead, I switched to\fontspec[Mapping=tex-text]{Arial}as recommended by the documentation and it magically works! – aardvarkk Feb 06 '14 at 20:52Mapping=tex-text, but same idea. – aardvarkk Feb 06 '14 at 21:17Ligatures=TeXthe default except when using\setmonofont. (Configurable, of course.) – Will Robertson Feb 07 '14 at 04:59