Including symbols in array

Don't iterate over control sequences. Instead build them from their names using \csname ... \endcsname:

\documentclass{article}
\usepackage{tikz}
\usepackage{wasysym}
\newcommand\planets{{"mercury","venus","mars","jupiter","saturn","uranus","neptune"}}
\begin{document}
% without using an array and pgfmathparse
\foreach \i in {mercury, venus,mars,jupiter,saturn,uranus,neptune}{
\csname\i\endcsname}

% using the array
\foreach \i in {0,...,6}{
\pgfmathparse{\planets[\i]}\csname\pgfmathresult\endcsname}

\end{document}

The planet symbol commands don't survive \edef, which is performed when \planets[\i] is evaluated.

You can avoid the problem by defining \planets with \noexpand in front of each item:

\documentclass{article}
\usepackage{pgffor}
\usepackage{wasysym}

\newcommand\planets{{%
  "\noexpand\mercury",%
  "\noexpand\venus",%
  "\noexpand\mars",%
  "\noexpand\jupiter",%
  "\noexpand\saturn",%
  "\noexpand\uranus",%
  "\noexpand\neptune"%
}}

\begin{document}

\foreach \i in {0,...,6}{\pgfmathparse{\planets[\i]}\pgfmathresult{} - }

\end{document}

However, if your aim is to be able to refer to a planet by its number, I suggest a different approach. The indexing starts at 1.

\documentclass{article}
\usepackage{xparse}
\usepackage{pgffor}
\usepackage{wasysym}

\ExplSyntaxOn
\NewExpandableDocumentCommand{\planet}{m}
 {
  \tl_item:nn { \mercury\venus\mars\jupiter\saturn\uranus\neptune } { #1 }
 }
\ExplSyntaxOff

\begin{document}

\foreach \i in {1,...,7}{\planet{\i} - }

\planet{3}

\end{document}