You don't want to typeset two consecutive spaces, in general. If your aim is to have larger space after periods, it's already built in TeX:
Some words. Other words.
\frenchspacing
Some words. Other words.
will produce

Note that \frenchspacing is not the default, so we have larger space after the period in the first line.
According to TeX's rules, a normal space is inserted, with an additional space with a value set for the font, because the \sfcode for the period is 3000 (greater than 2000); in the Computer Modern font the extra space is one third of the normal interword space.
If you really want a double space after a period, you have to change the font parameter, which is not an easy task because it should be done for every font in the document.
Here's how one could do, but please, don't.
\documentclass{article}
\usepackage{xpatch}
\makeatletter
\xpatchcmd{\selectfont}
{\pickup@font\font@name}
{\pickup@font\font@name\fontdimen7\font=\fontdimen2\font}
{}{}
\makeatother
\begin{document}
Some words. Other words.
\frenchspacing
Some words. Other words.
\end{document}

If you instead want to occasionally have a double space (also Knuth uses them somewhere in the TeXbook), use <space>\<space>:
[...] followed by the recent contributions beginning with the
page break. \ (Deep breath.) \ You got that?

wordusers have to add the spaces explicitly, which is prone to errors. LaTeX can add them automatically: just put\nonfrenchspacingin your preamble (this is the default). However, if you want a modern look of your document, just put\frenchspacingin your document preamble. This is what I recommend in LaTeX and Friends. – Jan 01 '13 at 19:43\frenchspacingis disabled. – Jan 01 '13 at 19:45\frenchspacingcontrols the amount of space added by TeX/LaTeX after a sentence independent from the number of spaces in the source code. However, putting two spaces in the source code can still be useful, as editors like Vi and Vim use them to provide navigation like "move to the end of the current sentence". – Christian Lindig Jan 01 '13 at 20:04