Allowing line break at ',' in inline math mode?

If the expression contains many commas then consider to break it into several math expressions, separated by commas. It reads like a list of math expressions. This way TeX can break the line.

To achieve line breaks after a comma, you could insert \allowbreak after the comma and before the next math symbol. If necessary, leave a blank after \allowbreak.

If you would like to have a document wide solution, you could redefine the comma. One solution, following the tip here would be:

\makeatletter
\def\old@comma{,}
\catcode`\,=13
\def,{%
  \ifmmode%
    \old@comma\discretionary{}{}{}%
  \else%
    \old@comma%
  \fi%
}
\makeatother

You could take a look at the breqn package, which is aimed at solving this problem in a general sense.

Here is a solution that doesn't make the comma globally active:

\documentclass{article}

\newcommand{\splitatcommas}[1]{%
  \begingroup
  \begingroup\lccode`~=`, \lowercase{\endgroup
    \edef~{\mathchar\the\mathcode`, \penalty0 \noexpand\hspace{0pt plus 1em}}%
  }\mathcode`,="8000 #1%
  \endgroup
}

\begin{document}

\setlength{\lineskiplimit}{2pt}\setlength{\lineskip}{3pt} % for this particular case

$\splitatcommas{
  \frac{1}{2},\frac{3}{5},\frac{8}{13},\frac{21}{34},\frac{55}{89},
  \frac{144}{233},\frac{377}{610},\frac{987}{1597},\frac{2584}{4181},
  \frac{6765}{10946},\frac{17711}{28657},\frac{46368}{75025},
  \frac{121393}{196418},\frac{317811}{514229},\frac{832040}{1346269},
  \frac{2178309}{3524578},\frac{5702887}{9227465},
  \frac{14930352}{24157817},\frac{39088169}{63245986},\frac{102334155}{165580141}
}$

\end{document}

The setting of \lineskiplimit and \lineskip are for the particular case where fractions are needed in the argument.

A variant that allows nesting:

\documentclass{article}

\newcommand{\splitatcommas}[1]{%
  \begingroup
  \ifnum\mathcode`,="8000
  \else
    \begingroup\lccode`~=`, \lowercase{\endgroup
      \edef~{\mathchar\the\mathcode`, \penalty0 \noexpand\hspace{0pt plus 1em}}%
    }\mathcode`,="8000
  \fi
  #1%
  \endgroup
}

\newcommand{\tuple}[1]{(\splitatcommas{#1})}
\newcommand{\set}[1]{\{\splitatcommas{#1}\}}

\begin{document}

\setlength{\lineskiplimit}{2pt}\setlength{\lineskip}{3pt} % for this particular case

$\splitatcommas{
  \frac{1}{2},\frac{3}{5},\frac{8}{13},\frac{21}{34},\frac{55}{89},
  \frac{144}{233},\frac{377}{610},\frac{987}{1597},\frac{2584}{4181},
  \frac{6765}{10946},\frac{17711}{28657},\frac{46368}{75025},
  \frac{121393}{196418},\frac{317811}{514229},\frac{832040}{1346269},
  \frac{2178309}{3524578},\frac{5702887}{9227465},
  \frac{14930352}{24157817},\frac{39088169}{63245986},\frac{102334155}{165580141}
}$

$\set{
  \tuple{a,b,c,d},\tuple{1,2,3,4,5,6},\tuple{11,22,33,44,55,66,77,88},
  \tuple{a,b,c,d},\tuple{1,2,3,4,5,6},\tuple{11,22,33,44,55,66,77,88},
  \tuple{a,b,c,d},\tuple{1,2,3,4,5,6},\tuple{11,22,33,44,55,66,77,88},
  \tuple{a,b,c,d},\tuple{1,2,3,4,5,6},\tuple{11,22,33,44,55,66,77,88}
}$

\end{document}