To only generate one label per bar stack, add the nodes near coords
option to the last series only, using \addplot +[nodes near coords] coordinates...
.
In order to place the labels at the end of the bars, and not in the middle of the bar, starting with PGFPlots version 1.9 you have to add nodes near coords xbar stacked configuration/.style={}
before calling xbar stacked
.
To print the sum of the bar stacks, instead of the value of the last bar part, starting with PGFPlots version 1.9 you have to add point meta=x
to your \addplot
options.

Code for PGFPlots >= 1.9:
\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}
\pgfplotsset{testbar/.style={
nodes near coords xbar stacked configuration/.style={},
xbar stacked,
width=.8\textwidth,
axis y line*= none, axis x line*= bottom,
xmajorgrids = true,
xmin=0,xmax=70,
ytick = data, yticklabels = {C1,C2},
tick align = outside, xtick pos = left,
bar width=6mm, y=8mm,
enlarge y limits={abs=0.625},% 0.5 + 0.5*(y - bar width)/y [TeX.sx #47995]
}}
\begin{document}
\begin{tikzpicture}
\begin{axis}[testbar]
\addplot coordinates{(2.68,1) (2.94,0)};
\addplot coordinates{(26.63,1) (31.67,0)};
\addplot +[
point meta=x,
nodes near coords,
nodes near coords align={anchor=west},
every node near coord/.append style={
black,
fill=white,
fill opacity=0.75,
text opacity=1,
outer sep=\pgflinewidth % so the label fill doesn't overlap the plot
}
]coordinates{(6.2,1) (9.91,0)};
\end{axis}
\end{tikzpicture}
\end{document}
Code for PGFPlots < 1.9:
\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{testbar/.style={
xbar stacked,
width=.8\textwidth,
axis y line*= none, axis x line*= bottom,
xmajorgrids = true,
xmin=0,xmax=70,
ytick = data, yticklabels = {C1,C2},
tick align = outside, xtick pos = left,
bar width=6mm, y=8mm,
enlarge y limits={abs=0.625},% 0.5 + 0.5*(y - bar width)/y [TeX.sx #47995]
}}
\begin{document}
\begin{tikzpicture}
\begin{axis}[testbar]
\addplot coordinates{(2.68,1) (2.94,0)};
\addplot coordinates{(26.63,1) (31.67,0)};
\addplot +[
nodes near coords,
nodes near coords align={horizontal},
every node near coord/.append style={
black,
fill=white,
fill opacity=0.75,
text opacity=1,
outer sep=\pgflinewidth % so the label fill doesn't overlap the plot
}
]coordinates{(6.2,1) (9.91,0)};
\end{axis}
\end{tikzpicture}
\end{document}