As you can see from the enlarged version, the equation is longer then \textwidth, hence cannot be centered. But, in general instead of TeX $$...$$, a LaTeX \[...\] (or other structure) should be used. See Why is \[ ... \] preferable to $$ ... $$?
\documentclass[10pt]{article}
\begin{document}
I have tried for over one hour now, in vain, on centering one equation. Why in the world is the equation not centered - i.e., so much margin on the left??
$$\frac{dX_{SS}}{dt}=\Lambda-\mu X_{SS}-\frac{\beta\bigg(X_{HS}+X_{HT}+X_{H+{T_T^{(1)}}}+X_{H+T_T^{(2)}}
+X_{H+T_T^{(3)}}\bigg)}{N}-\frac{\tau(X_{ST}+X_{HT})X_{SS}}{N}$$
I have tried for over one hour now, in vain, on centering one equation. Why in the world is the equation not centered - i.e., so much margin on the left??
\end{document}

But it is better to split too long equation:
\documentclass[10pt]{article}
\usepackage{amsmath}
\begin{document}
I have tried for over one hour now, in vain, on centering one equation. Why in the world is the equation not centered - i.e., so much margin on the left??
\begin{align*}
\frac{dX_{SS}}{dt}&=\Lambda-\mu X_{SS}-\frac{\beta\bigg(X_{HS}+X_{HT}+X_{H+{T_T^{(1)}}}+X_{H+T_T^{(2)}}
+X_{H+T_T^{(3)}}\bigg)}{N}\\
&\quad{}-\frac{\tau(X_{ST}+X_{HT})X_{SS}}{N}
\end{align*}
I have tried for over one hour now, in vain, on centering one equation. Why in the world is the equation not centered - i.e., so much margin on the left??
\end{document}

$$...$$for one-line displayed maths in LaTeX documents; use\[...\]instead (See http://tex.stackexchange.com/questions/503/why-is-preferable-to). – Gonzalo Medina Jul 17 '14 at 03:30