LaTeX equivalent of <br><br><br> in HTML?

LaTeX is for professional typesetting and doesn't allow you the freedom of HTML. Two line breaks in a row don't make any sense for typography. If you want to add more vertical space using the optional argument of \\[<extra vertical space to add>]. The distance of two lines is given by \baselineskip:

This is line one\\[2\baselineskip]
This is line two

You can also use \bigskip between paragraphs to add more vertical space between them. Note that there is a difference between line breaks and new paragraphs.

This is the last line of one paragraph.
\par% or empty line in the source code
\bigskip
This is the first line of the next paragraph.

You should separate paragraphs with blank lines. If, occasionally, you want an extra separation between two paragraphs you should use one of the \...skip commands, for example:

\noindent
This is the first paragraph.

\bigskip\noindent
This is the second paragraph.

Note that you wont be willing to do that too often, except for the occasional case. If you want to suppress indentation in all your paragraphs in your document, and leave a larger space between them, then use the parskip package

\documentclass{article}
\usepackage{parskip}
\begin{document}

This is the first paragraph.

This is the second paragraph.

\end{document}

If for some reason you really want “line breaks” (as opposed to “paragraph breaks”) then use \\, i.e.:

This is line one \\
. \\
. \\
This is line two

What is important to note is that \\ is for a premature line-break within a paragraph: it does not terminate the paragraph.

To add manual space between paragraphs, use \par\vspace{<dimen>}.