Longtable caption numbering

If the caption package is loaded anyway you can use the longtable* environment which does not increment the table counter. (See ltcaption package documentation for details.)

As opposite to \addtocounter{table}{-1} this solution does never make trouble when used with hyperref.

\documentclass[12pt]{article}
\usepackage{longtable}
\usepackage{caption}
\usepackage{hyperref}

\begin{document}
 First table is inserted here (longtable).
\begin{longtable*}{l l}
\hline
    A & A1 \\
    B & B1 \\   
\hline
%\caption*{Some text}
\end{longtable*}

\newpage
Second table inserted here.
\begin{table} 
\centering
\caption{Influence of X}\label{TableC}
...
\end{table}

\newpage
\listoftables 
\end{document}

Add

\addtocounter{table}{-1} 

inside the longtable environment. As Boris said in his answer, if you don't want a caption for the longtable, you can safely delete the \caption* and \label commands. A little example:

\documentclass{article}
\usepackage{longtable}

\begin{document}

 \begin{longtable}{l l}
   A1 & A2
   \addtocounter{table}{-1} 
\end{longtable}

\begin{table}
  \centering
  \caption{test table}
  \label{tab:test}
  \begin{tabular}{cc}
  text1 & text2
  \end{tabular}
\end{table}

\end{document}