One solution would be to add the title as part of the number using the number freestyle option:
\documentclass{article}
\usepackage{varioref}
\usepackage{cleveref}
\usepackage{tcolorbox}
\newtcolorbox[
auto counter,
number within=section,
number freestyle={\noexpand\thesection.\noexpand\arabic{\tcbcounter}~\noexpand\mytitle},
crefname={bluebox}{blueboxes}]%
{mybluebox}[2][]{
colback=blue!5!white,
colframe=blue!75!black,
fonttitle=\bfseries,
code={\def\mytitle{#2}},
title=Bluebox \thetcbcounter,%
#1}
\begin{document}
\section{Test}
\begin{mybluebox}[label={myreference}]{My title}
This is an example.
\end{mybluebox}
\Cref{myreference}
\end{document}

My Titlein the reference and, since I am usinghyperref,My Titleappears with thelinkcolor. How could I haveMy Titlethe same color asBlueboxnamely black? – schremmer Jun 04 '16 at 03:20\Cref{myreference}gets colored withlinkcolor... – Thomas F. Sturm Jun 06 '16 at 05:51