How to make listings code indentation remain unchanged when copied from PDF?

To prevent random spaces when copying the text from a listing, you need to use

\lstset{columns=flexible}

But you will now note that the text is not neatly aligned anymore; to solve this, you need to also use

\lstset{keepspaces=true}

This will not solve your problem with spaces disappearing at the beginning of lines when copying. The following hack will produce visible spaces and then make them invisible by coloring them in the background color:

\makeatletter
\def\lst@outputspace{{\ifx\lst@bkgcolor\empty\color{white}\else\lst@bkgcolor\fi\lst@visiblespace}}
\makeatother

This hack is not perfect, however, as the typesetted character is really a visible space, not a space (so searching the pdf for char line will not work) and some PDF readers (like Mac's preview) will copy a visible space. It works under Acrobat Reader and it's extremely pleasant to be able to quickly copy/paste code without problem (perhaps the problem can be circumvented by writing direct PDF code to tell that it's a space, I've never had the time to try). It might also not work with all typewriter fonts.

Here's the full code of your example:

\documentclass[12pt,oneside]{memoir}

\usepackage{listings}
\usepackage[T1]{fontenc}
\usepackage{xcolor}
\usepackage{textcomp}

\definecolor{codebg}{HTML}{EEEEEE}
\definecolor{codeframe}{HTML}{CCCCCC}

\lstset{language=Awk}
\lstset{backgroundcolor=\color{codebg}}
\lstset{frame=single}
\lstset{framesep=10pt}
\lstset{rulecolor=\color{codeframe}}
\lstset{upquote=true}
\lstset{basicstyle=\ttfamily}
\lstset{showstringspaces=false}

\lstset{columns=flexible}
\lstset{keepspaces=true}
\makeatletter
\def\lst@outputspace{{\ifx\lst@bkgcolor\empty\color{white}\else\lst@bkgcolor\fi\lst@visiblespace}}
\makeatother

\begin{document}

This code example prints out all users on your system:

\begin{lstlisting}[language=c]
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define MAX_LINE_LEN 1024

int main() {
    char line[MAX_LINE_LEN];
    FILE *in = fopen("/etc/passwd", "r");
    if (!in) exit(EXIT_FAILURE);

    while (fgets(line, MAX_LINE_LEN, in) != NULL) {
        char *sep = strchr(line, ':');
        if (!sep) exit(EXIT_FAILURE);
        *sep = '\0';
        printf("%s\n", line);
    }
    fclose(in);
    return EXIT_SUCCESS;
}
\end{lstlisting}

\end{document}

you can use the following modifcation

\newlength{\lstcolumnwidth}
\settowidth{\lstcolumnwidth}{\ttfamily M}
\lstset{basicstyle=\ttfamily,basewidth=\lstcolumnwidth,columns=fixed, fontadjust=true} 

The indention at the beginning of line isn't a problem by LaTeX. This is a problem of the reader. There are no settings for such case. You can get an odd solution with the following code:

\lstset{showspaces=true}
\makeatletter
\def\lst@visiblespace{\textcolor{codebg}{-}}
\makeatother

With packages like attachefile2 you can attach the original c-file.

My answer will not answer your question. :-) But I have a good way to manage code snippet inclusion to be easily accessible for the readers. Rather than copying the code from the pdf, it will be better if you allow the readers to open the underlying code file by clicking hyperlinks.

Try compile the following code. I use latex-dvips-ps2pdf compilation steps. You can use pdflatex of course, but don't forget to remove dvips option in \documentclass.

For the sake of easy maintainability, create your own package as follows:

\NeedsTeXFormat{LaTeX2e}[1994/06/01] 
\ProvidesPackage{xport}[2011/06/05 v0.01 LaTeX package for my own purpose]  
\RequirePackage[utf8x]{inputenc}
\RequirePackage{xcolor}

\RequirePackage{caption}
\captionsetup
{%
   font={small,rm},
   labelfont={color=Maroon,bf},
   justification=justified%
}

\RequirePackage{listings}
\AtBeginDocument
{%
    \renewcommand*{\lstlistlistingname}{Code List}%
    \renewcommand*{\lstlistingname}{Code}%
}

\lstset
{%
        %linewidth=\linewidth,  
        breaklines=true,
        tabsize=3, 
        showstringspaces=false%      
}


\lstdefinestyle{Common}
{%
        extendedchars=\true,
        language={[Sharp]C},
        %alsolanguage={PSTricks},
        frame=single,   
        %===========================================================
        framesep=3pt,%expand outward.
        framerule=0.4pt,%expand outward.
        xleftmargin=3.4pt,%make the frame fits in the text area. 
        xrightmargin=3.4pt,%make the frame fits in the text area.
        %=========================================================== 
        rulecolor=\color{Red}%
}

\lstdefinestyle{A}%
{%
        style=Common,
        backgroundcolor=\color{Yellow!10},
        basicstyle=\scriptsize\color{Black}\ttfamily,
        keywordstyle=\color{Orange},
        identifierstyle=\color{Cyan},
        stringstyle=\color{Red}, 
        commentstyle=\color{Green}% 
}

\newcommand{\IncludeCSharp}[2][style=A]%
{%
    \lstinputlisting[#1,caption={\href{#2}{#2}}]{#2}%
}

%for beamer, use \hypersetup instead.
\RequirePackage[colorlinks=true,bookmarksnumbered=true,bookmarksopen=true]{hyperref}

%to make hyperlinks point to the top of figure or table.
%it must be loaded after hyperref.
\RequirePackage[all]{hypcap}% cannot be used in beamer.

\endinput 

In the main input file, you can call \IncludeCSharp as follows:

\documentclass[dvips,dvipsnames,cmyk,12pt]{article}
\usepackage[a4paper,margin=2cm]{geometry}
\usepackage{xport}
\begin{document}

\IncludeCSharp[style=A]{Codes/Program.cs}    

\end{document}

The imported C# file is named Program.cs in Codes/ sub directory.

using System;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine("Hello World!");//This is a comment.
            /*This is a comment too.*/
        }
    }
}