Align the baselines of two nodes placed side by side

You should just \smash the [b]aseline of those words/phrases:

\documentclass{article}

\usepackage{tikz,amsmath}

\begin{document}

\usetikzlibrary{positioning,calc}
\tikzstyle{block} = [draw, rectangle, minimum height=1cm, minimum width=1cm, outer sep=0pt]

\begin{tikzpicture}
  \node [block,align=center](A) {\shortstack{double \\ type}};
  \node [block,align=center,right=1.5cm of A](B) {\shortstack{\smash[b]{single} \\ type}};
\end{tikzpicture}

\end{document}

amsmath provides the extended version of \smash.

Another method is to use the \NextLine macro instead of \\. This eliminates the need to go back and change things just because you changed the text:

References

• How to make mdframed ignore descenders in last line

Code:

\documentclass[crop,tikz, border=2pt]{standalone}
\begin{document}

%% https://tex.stackexchange.com/a/51406/4301
\newcommand*{\IgnodeDescenders}{-\dimexpr\dp\strutbox+\baselineskip}
\newcommand*{\NextLine}{\strut\\[\IgnodeDescenders]}

\usetikzlibrary{positioning,calc}
\tikzstyle{block} = [draw, rectangle, minimum height=1cm, minimum width=1cm, outer sep=0pt]

\begin{tikzpicture}
\node [block,align=center](A) {\shortstack{double\NextLine type}};
\node [block,align=center,right=1.5cm of A](B) {\shortstack{single\NextLine type}};

\end{tikzpicture}
\end{document}

This is discussed at length in the pgfmanual on p. 65. The upshot is that you can add a suitable text depth.

\documentclass[crop,tikz]{standalone}
\begin{document}

\usetikzlibrary{positioning,calc}
\tikzset{block/.style={draw, rectangle, minimum height=1cm, minimum width=1cm,
outer sep=0pt,text height=3ex,text depth=.25ex}}

\begin{tikzpicture}
\node [block,align=center](A) { double \\ type };
\node [block,align=center,right=1.5cm of A](B) {single \\ type };
\draw[red] (A.west) -- (B.east);
\end{tikzpicture}
\end{document}

The red line is only to guide the eye.