How to define a command that takes more than 9 arguments

You are going to have to parse the arguments some at a time and store them into temporary registers or macros. For example

\newcommand\foo[9]{%
    \def\tempa{#1}%
    \def\tempb{#2}%
    \def\tempc{#3}%
    \def\tempd{#4}%
    \def\tempe{#5}%
    \def\tempf{#6}%
    \def\tempg{#7}%
    \def\temph{#8}%
    \def\tempi{#9}%
    \foocontinued
}
\newcommand\foocontinued[7]{%
    % Do whatever you want with your 9+7 arguments here.
}

There's the xargs package, and there's also some black TeX magic. As for myself, being conditioned in Python, I prefer the key-value parameter syntax provided by keyval/xkeyval packages.

On an unrelated note, if I find myself needing more than 9 parameters, that usually means that my macro/def/code organization is not very good, and I'd try to improve that first. But of course, there are legitimate situations where 9 parameters are perfectly okay --- especially if you try to build a definition with a lot of knobs and tweaks.

NEW ANSWER

The listofitems package used here is preferable to my original answers below, because \readlist does not expand the argument when capturing it, nor does it rely on inconvenient roman-numeral syntax.

\documentclass{article}
\usepackage{listofitems}
\begin{document}
\setsepchar{ }
\readlist\arg{1 2 3 4 5 6 7 8 9 10 11 12 FinalArgument}
There are \arglen{} arguments.  The thirteenth is \arg[13]
\end{document}

ORIGINAL ANSWER

In a response to How to use variables inside a command when generating a table? I mention how the stringstrings package has a \getargs command that will parse large numbers of arguments that are passed within a single { }. To recap that reply,

\documentclass{article}
\usepackage{stringstrings}
\begin{document}
\getargs{1 2 3 4 5 6 7 8 9 10 11 12 FinalArgument}
There are \narg~arguments.  The thirteenth is \argxiii
\end{document}

The result to this example is:

There are 13 arguments. The thirteenth is FinalArgument

---

EDIT: A much more efficient version of \getargs is available in the readarray package and called \getargsC (in deference to David Carlisle's help). Thus, the same task can be accomplished more quickly with

\documentclass{article}
\usepackage{readarray}
\begin{document}
\getargsC{1 2 3 4 5 6 7 8 9 10 11 12 FinalArgument}
There are \narg~arguments.  The thirteenth is \argxiii
\end{document}