Suppress page numbers in article documentclass

You need to set the page style after \maketitle since \maketitle sets the page using \thispagestyle{plain} (which overwrites your request for it to be empty):

\documentclass[a4paper,10pt,english]{article}
\title{My title}
\begin{document}
 \maketitle
 \thispagestyle{empty}% Reset page style to 'empty'
 Hello World
\end{document}

If you wish to suppress the page numbering for all pages within your article, you should add \pagestyle{empty} to your document preamble.

The article document class also supports the titlepage option, which typesets an entire page (a titlepage) when using \maketitle. Such a page is necessarily issued using \thispagestyle{empty}. That is, without any header/footer.

To suppress page numbers on every page regardless of the page style(s) used by the document class, add \pagenumbering{gobble} to your preamble.

\pagenumbering{gobble} will interact badly with hyperref if you have links going from the citations to the page numbers

On the other hand it can be a hassle to have to redefine the pagestyle after \maketitle in the document instead of having all your styles defined in the preamble.

To have the best of both words you can put in the preamble:

\pagestyle{empty}
\let\svmaketitle\maketitle
\def\maketitle{\svmaketitle\thispagestyle{empty}}

which will patch the \maketitle command to set the empty page style automatically.