Is there a ditto symbol?

You are referring to the ditto mark, which is actually a special Unicode character (U+3003) looking like this:

Unicode Character 'DITTO MARK' (U+3003): 〃

Using XeLaTeX or LuaLaTeX, you could use this character directly, provided that you use a font the has support for this symbol. However, the Wikipedia article cited above mentions that

[...] in practice closing double quotation marks (”) or straight double quotation marks (") are often used instead [of the Unicode symbol]

so you might as well use something like

\newcommand*{\dittoclosing}{---''---}
\newcommand*{\dittostraight}{---\textquotedbl---} % available in T1 encoding

(The latter requires you to use \usepackage[T1]{fontenc}).

The result looks like this:

The german Wikipedia claims that the Unicode DITTO MARK is for CJK languages only … Furthermore I’d add some space around the quotation marks and lower them a little. In my eyes the qoute version don’t look very good. I like a TikZ version, as the following, since the vertical bars math the horizontal ones better … In most cases I prefer repeated text, though.

\documentclass{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}

\newcommand*{\dittoclosing}{--- \raisebox{-0.5ex}{''} ---}


\usepackage{tikz}
\newcommand{\dittotikz}{%
    \tikz{
        \draw [line width=0.12ex] (-0.2ex,0) -- +(0,0.8ex)
            (0.2ex,0) -- +(0,0.8ex);
        \draw [line width=0.08ex] (-0.6ex,0.4ex) -- +(-1.5em,0)
            (0.6ex,0.4ex) -- +(1.5em,0);
    }%
}


\begin{document}
\begin{tabular}{ll}
Some long stupid text & Text A \\
\dittoclosing & Text B \\
\end{tabular}

\begin{tabular}{ll}
Some long stupid text & Text A \\
\dittotikz & Text B \\
\end{tabular}
\end{document}