How to suppress caption numbering in a table?

You can suppress the caption label in saveral ways using features provided by the caption package:

1. Using \caption* instead of \caption:

   \documentclass{article}
   \usepackage{caption}
   
   \begin{document}
   
   \begin{table}[h]
     \centering
     \begin{tabular}{c} 
       text1\\
       text2
     \end{tabular}
     \caption*{This is my caption.}
   \end{table}
   
   \end{document}
   

2. Using the option labelformat=empty for \captionsetup.

   \documentclass{article}
   \usepackage{caption}
   
   \captionsetup[table]{labelformat=empty}
   
   \begin{document}
   
   \begin{table}[h]
     \centering
     \begin{tabular}{c} 
       text1\\
       text2
     \end{tabular}
     \caption{This is my caption.}
   \end{table}
   
   \end{document}
   

Since I used table as optional argument for \captionsetup, this change will only affect the table environments; of course, you can use figure instead (to affect only the figure environment), or no optional argument at all, which means that the change will affect all your floating objects.

Also, as I used \captionsetup in the preamble, the change will affect all the (in this case) table environments in your document; if you want the change to affect only a particular table environment, you can use

\captionsetup{labelformat=empty} 

inside that particular table environment.

The result after compilation of any of my example codes is

Use the caption package to control the look and feel of the captions:

\documentclass{article}
\usepackage{caption}
\begin{document}
\section{Data}
\begin{table}[h]
\centering
\begin{tabular}{lcccc}  
...table content...
\end{tabular}
\caption*{This is my caption.}
\end{table}
\end{document}

The memoir class (caters for the book, report, and article classes) incudes the \legend macro

\legend{text}

which can be used to put an anonymous caption, or legend, into a float environment but it can be used anywhere, such as in a marginal note.

See section Continuation captions and legends in the manual (> texdoc memoir)