How to wrap text in LaTeX tables?

Use p{width} for your column specifiers instead of l/r/c.

\begin{tabular}{|p{1cm}|p{3cm}|}
  This text will be wrapped & Some more text \\
\end{tabular}

EDIT: (based on the comments)

\begin{table}[ht]
    \centering
    \begin{tabular}{p{0.35\linewidth} | p{0.6\linewidth}}
      Column 1  & Column2 \\ \hline
      This text will be wrapped & Some more text \\
      Some text here & This text maybe wrapped here if its tooooo long \\
    \end{tabular}
    \caption{Caption}
    \label{tab:my_label}
\end{table}

we get:

With the regular tabular environment, you want to use the p{width} column type, as marcog indicates. But that forces you to give explicit widths.

Another solution is the tabularx environment:

\usepackage{tabularx}
...
\begin{tabularx}{\linewidth}{ r X }
    right-aligned foo & long long line of blah blah that will wrap when the table fills the column width\\
\end{tabularx}

All X columns get the same width. You can influence this by setting \hsize in the format declaration:

>{\setlength\hsize{.5\hsize}} X >{\setlength\hsize{1.5\hsize}} X

but then all the factors have to sum up to 1, I suppose (I took this from the LaTeX companion). There is also the package tabulary which will adjust column widths to balance row heights. For the details, you can get the documentation for each package with texdoc tabulary (in TeXlive).

Another option is to insert a minipage in each cell where text wrapping is desired, e.g.:

\begin{table}[H]
\begin{tabular}{l}
\begin{minipage}[t]{0.8\columnwidth}%
a very long line a very long line a very long line a very long line
a very long line a very long line a very long line a very long line
a very long line a very long line a very long line %
\end{minipage}\tabularnewline
\end{tabular}
\end{table}

Simple like a piece of CAKE!

You can define a new column type like (L in this case) while maintaining the current alignment (c, r or l):

\documentclass{article}
\usepackage{array}
\newcolumntype{L}{>{\centering\arraybackslash}m{3cm}}

\begin{document}

\begin{table}
    \begin{tabular}{|c|L|L|}
        \hline
        Title 1 & Title 2 & Title 3 \\
        \hline 
        one-liner & multi-line and centered & \multicolumn{1}{m{3cm}|}{multi-line piece of text to show case a multi-line and justified cell}   \\
        \hline
        apple & orange & banana \\
        \hline
        apple & orange & banana \\
        \hline
    \end{tabular}
\end{table}
\end{document}

To change the text AB into A \r B in a table cell, put this into the cell position: \makecell{A \\ B}.

Before doing that, you also need to include package makecell.

The new tabularray makes wrapping text in cells easier then ever before.

The package supports all the traditional used column names like c, l, r, etc., but also has its own Q column which accepts various keys to control the width and vertical and horizontal alignment. It also provides an X column, as known from tabularx` which will automatically calculate the width of the column to fit the table into the available text width.

Another nice feature is that all the settings can also be done for individual cells.

\documentclass{article}
\usepackage{tabularray}

\begin{document}

\begin{table}
    \begin{tblr}{|c|Q[2cm,valign=m]|X[j,valign=m]|}
        \hline
        Title 1 & Title 2 & Title 3 \\
        \hline 
        one-liner & multi-line text & multi-line piece of text to show case a multi-line and justified cell   \\
        \hline
        apple & orange & banana \\
        \hline
        \SetCell{h,2cm} wrapping text only in a single cell & orange & banana \\
        \hline
    \end{tblr}
\end{table}
\end{document}

(thanks to Shayan Amani for providing a MWE in their answer!)