
I'd like to produce two sets of curly brackets around three lines of text, one beneath the other and a short line in between on the left. Hope this is clear enough. Apologies for the terrible pic.

I'd like to produce two sets of curly brackets around three lines of text, one beneath the other and a short line in between on the left. Hope this is clear enough. Apologies for the terrible pic.
Is this something like you'd like to obtain?
\documentclass{article}
\usepackage{booktabs}
\begin{document}
\begin{center}
Some text on the left
$\begin{array}{@{}l@{}c@{}}
\quad&\left\{
\begin{tabular}{@{}l@{}}
A line \\
A longer line \\
Another
\end{tabular}
\right\}
\\
\cmidrule{1-1}
&\left\{
\begin{tabular}{@{}l@{}}
A line \\
A longer line \\
Another
\end{tabular}
\right\}
\end{array}$
\end{center}
\end{document}

A better implementation (but using low level commands), that should have no problems even when the two parts have different number of lines.
\documentclass{article}
\newcommand{\topbottombraced}[2]{%
\raise.5ex\vtop{
\vbox{%
\hbox{$\left\{\begin{tabular}{@{}l@{}}#1\end{tabular}\right\}$}
\vskip1pt
}
\vbox{%
\vskip1pt
\hbox{$\left\{\begin{tabular}{@{}l@{}}#2\end{tabular}\right\}$}
}
}%
}
\begin{document}
Some text on the left
\topbottombraced{
A line \\
A longer line \\
And another
}{
A line \\
A longer line \\
Another
}
\topbottombraced{
A line \\
A longer line \\
A longer line \\
A longer line \\
And another
}{
A line \\
A longer line \\
Another
}
\topbottombraced{
A line \\
A longer line \\
And another
}{
A line \\
A longer line \\
A longer line \\
A longer line \\
Another
}
\end{document}

{...} (when A longer line differs from top/bottom), use a fixed-width column like p{7em} for the inner tabulars.
– Werner
Dec 30 '14 at 23:40
A solution with the blkarray package:
\documentclass{article}
\usepackage{amsmath}
\usepackage{blkarray}%
\usepackage{xcolor}
\begin{document}
\renewcommand{\arraystretch}{1.3}
\[
\text{
\raisebox{3ex}{Shakespeare wrote}\quad
\begin{blockarray}{l}
\begin{block}{\{>{\enspace}l<{\,}\}}
Shall I compare thee to a summer's day?\\
Thou art more lovely and more temperate.\\
Rough winds do shake the darling buds of May,\\
And summer’s lease hath all too short a date.\\
Sometime too hot the eye of heaven shines,\\
And often is his gold complexion dimmed;\\
And every fair from fair sometime declines,\\
\end{block}
\begin{block}{\{>{\enspace}l<{\,}\}}
By chance, or nature’s changing course, untrimmed;\\
But thy eternal summer shall not fade,\\
Nor lose possession of that fair thou ow’st,\\
Nor shall death brag thou wand’rest in his shade,\\
When in eternal lines to Time thou grow’st.\\
So long as men can breathe, or eyes can see,\\
So long lives this, and this gives life to thee.\\
\end{block}\\
\end{blockarray}}
\]
\end{document}

This uses stacks, and has no problem at all if the top and bottom halves have different numbers of entries.
\documentclass{article}
\usepackage[usestackEOL]{stackengine}
\begin{document}
This is baseline text
\strutlongstacks{T}%
\renewcommand\stackalignment{l}%
\stackunder[0pt]{\stackon[5pt]{}%
{$\left\{\setstackgap{L}{12pt}\Centerstack{%
first line\\second line\\third line}\right\}$}
}%
{$\left\{\setstackgap{L}{12pt}\Centerstack{%
first line\\second line of text\\third line\\fourth line}\right\}$}
\end{document}

In follow up comments, the OP inquired about the use of stacks in tabular. There arise only 2 quirks to doing so: 1) tabular redefines \baselineskip, and so the long-stack gap must be set to an explicit value, as in \setstackgap{L}{12pt}; and 2) I use \addstackgap{} to provide vertical buffer above/below the stack.
\documentclass{article}
\usepackage[usestackEOL]{stackengine}
\setstackgap{L}{12pt}
\begin{document}
\begin{tabular}{|c|c|}
\hline
\Centerstack{This is split\\ baseline text}
\strutlongstacks{T}%
\renewcommand\stackalignment{l}%
\addstackgap{%
\stackunder[-1pt]{\stackon[6pt]{}%
{$\left\{\setstackgap{L}{12pt}\Centerstack{%
first line\\second line\\third line}\right\}$}
}%
{$\left\{\setstackgap{L}{12pt}\Centerstack{%
first line\\second line of text\\third line\\fourth line}\right\}$}}
& blah blah\\
\hline
\end{tabular}
\end{document}

\Centerstack[l]{This is\\ baseline text} prior to the braced material. You might need to tweak the stacking gaps [0pt] and [5pt] to suit.
– Steven B. Segletes
Jan 03 '15 at 23:44
tabular environments, but there is a catch. Long stacks have, by default, an interbaseline skip of \baselineskip, which is redefined by tabular. Thus, before entering the tabular, you must redefine the long stack gap in explicit units, such as \setstackgap{L}{12pt}. Does this help?
– Steven B. Segletes
Jan 04 '15 at 16:53
\usepackage{booktabs}
\begin{document}
\begin{center} \setstackgap{L}{12pt} Some text on the left $\begin{array}{@{}l@{}c@{}} \quad&\left{ \begin{tabular}{@{}l@{}} A line \ A longer line \ Another \end{tabular} \right} \ \cmidrule{1-1} &\left{ \begin{tabular}{@{}l@{}} A line \ A longer line \ Another \end{tabular} \right} \end{array}$ \end{center}
\end{document}
– Guillaume Coatalen Jan 04 '15 at 17:42\usepackage[usestackEOL]{stackengine}. Add that and your example compiles for me. You can find the package documentation at http://ctan.org/pkg/stackengine.
– Steven B. Segletes
Jan 04 '15 at 21:15
tabular.
– Steven B. Segletes
Jan 05 '15 at 12:53
\textmd{} to override the bolding.
– Steven B. Segletes
Oct 18 '15 at 15:13
If you need math-mode inside braces:
\def\bmatrix#1{\left\{\matrix{#1}\right\}}
$$
a + b + \cdots + f = \matrix{\bmatrix{a\cr b\cr c}\cr\bmatrix{d\cr e\cr f}}
$$
If you need text-mode inside braces:
\def\btext#1{\left\{\vcenter{\halign{##\strut\hfil\cr#1\crcr}}\right\}}
$$
a + b + \cdots + f = \matrix{\btext{aha\cr be\cr cc}\cr \btext{dee\cr e\cr ef\cr}}
$$
If you need to center two braced texts with different lines:
\def\centertwo#1#2{\raise\fontdimen22\textfont2\vtop{\vbox{\hbox{$#1$}\kern0pt}\hbox{$#2$}}}
$$
a + b + \cdots + f = \centertwo {\btext{aha\cr be}} {\btext{dee\cr e\cr ef}}
$$
\bye
Note. Your question was not mention LaTeX as desired macro pckage. My macros work in plain TeX.