Whitespace around characters

The following might be in line with what you're after:

\documentclass{article}
\usepackage{amsmath,array}% http://ctan.org/pkg/{amsmath,array}
\newcolumntype{C}{>{{}}c<{{}}}
\begin{document}
\begin{align*}
  x = 1 + 2 + 3 + 4 + \cdots + n \\
  x = n + (n-1) + (n-2) + (n-3)+\cdots+ 1\\
  \cline{1-2}
  2x = (1+n) + (1+n) + (1+n) + (1+n) + \cdots (1+n)
\end{align*}

\[
  \renewcommand{\arraystretch}{1.2}
  \begin{array}{r*{12}{@{}C}}
    x & = & 1 & + & 2 & + & 3 & + & 4 & + & \cdots & + & n \\
    x & = & n & + & (n-1) & + & (n-2) & + & (n-3) & + & \cdots & + & 1 \\
    \hline
    2x & = & (1 + n) & + & (1 + n) & + & (1 + n) & + & (1 + n) & + & \cdots & + & (1+n)
  \end{array}
\]
\end{document}

The entire structure is set in an array with a column type that provides the appropriate spacing around binary operators and relations (by inserting an empty group {} on the left/right of every cell, thanks to the array package's \newcolumntype). Some extra padding on the left and right (default of \arraycolsep or 5pt) can be changed, if needed.

Do you mean something like this?

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{align*}
x &= 1 &&+ 2 &&+ 3 &&+ 4 &&+ \cdots &&+ n \\
x &= n &&+ (n-1) &&+ (n-2) &&+ (n-3)&&+\cdots&&+ 1\\
\cline{1-12}
2x &= (1+n) &&+ (1+n) &&+ (1+n) &&+ (1+n) &&+ \cdots &&+(1+n)
\end{align*}
\end{document}