The problem is that the spanish module for babel makes > and < active characters for its special management of Spanish quotations.
Update:
With PGF/TikZ version 3.0.0 there's a babel library that solves the problems produced by changes to category codes made by some babel modules, so it's enough to load the library:
\documentclass[spanish]{article}
\usepackage{babel}
\usepackage{tikz}
\usetikzlibrary{babel}
\begin{document}
Simple arrows:
\begin{tikzpicture}
\draw[->] (-1.5,0) -- (1.5,0);
\end{tikzpicture}
\tikz\draw[->] (-1.5,0) -- (1.5,0);
\end{document}
(Thanks to Claudio Fiandrino for pointing this out in his comment).
PGF/TikZ version 2.10
To deactivate the undesired redefinition for tikzpictures, but maintaining it for other parts of the document, you can use
execute at begin picture={\deactivatequoting},
execute at end picture={\activatequoting}
for every tikzpicture. Notice that this approach has two advantages:
No extra packages are required.
It also produces the desired result when using the command version \tikz (see example code below).
The code:
\documentclass[spanish]{article}
\usepackage{babel}
\usepackage{tikz}
\tikzset{
every picture/.append style={
execute at begin picture={\deactivatequoting},
execute at end picture={\activatequoting}
}
}
\begin{document}
Simple arrows:
\begin{tikzpicture}
\draw[->] (-1.5,0) -- (1.5,0);
\end{tikzpicture}
\tikz\draw[->] (-1.5,0) -- (1.5,0);
\end{document}

As a side note, don't use pdftex option; modern LaTeX systems detect the driver automatically.
\usepackage[english]{babel}works, but\usepackage[spanish]{babel}does not. Also, not sure why you have[pdftex,spanish]options for\documentclass- FYI, I am not that familiar withbabel. – Peter Grill Mar 20 '14 at 23:08\shorthandoff{>}\shorthandoff{<}after\begin{document}. < and > are active characters in Spanish. – Malipivo Mar 20 '14 at 23:13pdftexoption is not necessary with modern LaTeX systems (the driver is automatically detected). Using the idiomatic localization (spanish, in this case) as class option has the advantage that all language-sensitive packages (for example,babel,cleveref) that can eventually be loaded will pick it and produce the idiomatic localizations. – Gonzalo Medina Mar 20 '14 at 23:49