Greek text copy & paste fails

This could be an issue with your pdf viewer. For me, copy-paste works fine with your MWE (compiled with pdflatex) when viewed in Evince, but with Acrobat Reader I get the behaviour you describe.

Both viewers work on my machine when I use xelatex instead of pdflatex, which allows you to explicitly define a font. MWE below, note that a Linux font is used here (change to, for example, DejaVuSans in Windows).

\documentclass{article}
\usepackage{fontspec}
\newfontfamily\greekfont[Script=Greek]{Linux Libertine O}
\newfontfamily\greekfontsf[Script=Greek]{Linux Libertine O}
\usepackage{polyglossia}
\setdefaultlanguage{greek}
\title{Εξισορρόπηση διπλού ανάστροφου εκκρεμούς}
\begin{document}
\maketitle
\end{document}

Don't use utf8x and also add the bits I show below; then also Adobe Reader seems to be happy.

\input{glyphtounicode}
\pdfgentounicode=1

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[english,greek]{babel}
\title{Εξισορρόπηση διπλού ανάστροφου εκκρεμούς}
\begin{document}
\maketitle
\end{document}