Can one TeX file output to multiple PDF files?

How do you store this information? You could just have one info-file for each letter

% letter1.adr
\def\toname{Foo}

and

% letter2.adr
\def\toname{Bar}

and then have a main file

% main.tex
\documentclass[addrfield]{scrlttr2}
\input \jobname.adr

\begin{document}
\begin{letter}{\toname}
\opening{Dear \toname, }
 A nice letter.
\end{letter}
\end{document}

Then you can compile all letters from the command line with something like

for %i in (*.adr) do pdflatex -jobname=%i main.tex

The koma bundle also provides tools for more sophisticated address files.

Yes it is possible if you enable \write18 (e.g. pdflatex --shell-escape with MiKTeX). Then you can call pdflatex again inside your document. An example (the code is not from me). It will generate three documents \jobname1-\jobname3:

Case insensitive operating systems (e.g. Windows/MacOS)

\documentclass{article}

\ifx\conditionmacro\undefined
  \immediate\write18{%
    pdfLaTeX --jobname="\jobname1"
    \gdef\string\conditionmacro{1}\string\input\space\jobname
  }%
  \immediate\write18{%
    pdfLaTeX --jobname="\jobname2"
    \gdef\string\conditionmacro{2}\string\input\space\jobname
  }%
  \immediate\write18{%
    pdfLaTeX --jobname="\jobname3"
    \gdef\string\conditionmacro{3}\string\input\space\jobname
  }%
  \expandafter\stop
\fi

\begin{document}
\ifnum\conditionmacro=1 Condition is 1\fi
\ifnum\conditionmacro=2 Condition is 2\fi
\ifnum\conditionmacro=3 Condition is 3\fi

\verb|\conditionmacro| is \texttt{\meaning\conditionmacro}.
\end{document}

Case sensitive operating systems (e.g. Linux)

As noted in Martin Heller's comment you need to change this code for case sensitive operating systems to:

\documentclass{article}

\ifx\conditionmacro\undefined
  \immediate\write18{%
    pdflatex --jobname="\jobname1"
    "\gdef\string\conditionmacro{1}\string\input\space\jobname"
  }%
  \immediate\write18{%
    pdflatex --jobname="\jobname2"
    "\gdef\string\conditionmacro{2}\string\input\space\jobname"
  }%
  \immediate\write18{%
    pdflatex --jobname="\jobname3"
    "\gdef\string\conditionmacro{3}\string\input\space\jobname"
  }%
  \expandafter\stop
\fi

\begin{document}

\ifnum\conditionmacro=1 Condition is 1\fi 

\ifnum\conditionmacro=2 Condition is 2\fi

\ifnum\conditionmacro=3 Condition is 3\fi

\verb|\conditionmacro| is \texttt{\meaning\conditionmacro}.

\end{document}

Edit for lualatex

in newer luatex version \write18 has no special meaning anymore and can't be used like this. You then need the shellesc package which overloads \write. It also offers a \ShellEscape which can be used (also with pdflatex) instead of the primitive commands. The example looks then like this.

\documentclass{article}
\usepackage{shellesc}
\ifx\conditionmacro\undefined
  \ShellEscape{%
    lualatex --jobname="\jobname1"
    "\gdef\string\conditionmacro{1}\string\input\space\jobname"
  }%
  \ShellEscape{%
    lualatex --jobname="\jobname2"
    "\gdef\string\conditionmacro{2}\string\input\space\jobname"
  }%
  \ShellEscape{%
    lualatex --jobname="\jobname3"
    "\gdef\string\conditionmacro{3}\string\input\space\jobname"
  }%
  \expandafter\stop
\fi

\begin{document}

\ifnum\conditionmacro=1 Condition is 1\fi

\ifnum\conditionmacro=2 Condition is 2\fi

\ifnum\conditionmacro=3 Condition is 3\fi

\verb|\conditionmacro| is \texttt{\meaning\conditionmacro}.

\end{document}

The answer is no, TeX outputs one PDF file.

I'd use a tool to split the PDF files afterwards. pdfpages (TeX) pdfsam, and pdftk should do the trick.