How to align node labels in tikz vertically if one of the labels has a superscript?

One way is to use [anchor=base] and add a \vphantom{X} node on the left to get the correct vertical spacing and a \hphantom{\widetilde{X} to get the correct horizontal spacing:

\node  [anchor=base] at (0,0)  {$\widetilde{X}$};
\node  [anchor=base] at (0,0) (input) {$\vphantom{X}\hphantom{\widetilde{X}}$};

which yields:

Note:

• I replaced the \tikzstyle with \tikzset which should be used instead: Should \tikzset or \tikzstyle be used to define TikZ styles?

Code:

\documentclass{standalone}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
    \tikzset{sum/.style={draw, shape=circle, node distance=1.5cm, line width=1pt, minimum width=1.5em}}

    %Creating Blocks and Connection Nodes
    \node  [anchor=base] at (0,0)  {$\widetilde{X}$};
    \node  [anchor=base] at (0,0) (input) {$\vphantom{X}\hphantom{\widetilde{X}}$};
    \node [sum, right of=input] (sum) {};
    \node at (sum) (plus) {{\footnotesize$+$}};
    \node at (1.5,-1) (noise) {$Z$};
    \node [anchor=base] at (3,0) (output) {$X$};

    %Lines
    \draw[->] (input.east) -- (sum);
    \draw[->] (noise) -- (sum.south);
    \draw[->] (sum) -- (output);
\end{tikzpicture}
\end{document}

Another possibilities: defining text height and text depth:

\begin{document}
\begin{tikzpicture}
    \tikzset{
node distance = 8mm and 12mm,
   sum/.style = {shape=circle, draw, line width=1pt, 
                 node contents={\huge$+$}},
N/.style = {text height=2ex, text depth=0.5ex}
            }
% nodes
\node (in)      [N]             {$\widetilde{X}$};
\node (sum)     [sum, right=of in];
\node (out)     [N,right=of sum]  {\vphantom{$\widetilde{X}$}$X$};
\node (noise)   [below=of sum]  {$Z$};
% lines
\draw[->] (in)      -- (sum);
\draw[->] (noise)   -- (sum);
\draw[->] (sum)     -- (out);
\end{tikzpicture}
\end{document}