Inclusion of images in a LaTeX document does not alter them at all, whether clipping or not. As such, if you want smaller output files you'll either need to pre-process the images or post-process the PDF file. It's important to note that as clipping is purely an effect on the appearance of the PDF, you should not use it to 'hide' anything you don't want people to see. Anyone interested enough will be able to find it inside the PDF.
Your preamble has several sins; but that's not the problem. If you type
\fbox{\includegraphics[scale=0.150,angle=0]{imagefilename.eps}}
TeX will add a frame and you'll realize that the figure has wide blank space around the main part:
How can you do? Add the trim option; I tried
\includegraphics[scale=0.150,trim=300 450 300 500,clip]{imagefilename.eps}
and the result is
(still with \fbox to show better the image, remove it when you're satisfied). The four parameters are the length (in PostScript points) to trim from the four sides in the order “left bottom right top”.
Here's a polished version of your document with some comments.
\documentclass[12pt,a4paper,twoside,openany]{report}
%%% language part
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\usepackage[spanish]{babel}
%%% page geometry
\usepackage[left=2.5cm,top=2.5cm,right=2.5cm,bottom=2.5cm]{geometry}
%%% fonts
\usepackage{mathptmx} % times is obsolete
\usepackage{courier}
\usepackage{eufrak}
%%% misc packages
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{multirow}
\usepackage{float}
\usepackage{color}
\usepackage{fancyhdr}
\usepackage{adjustbox}
\usepackage{enumerate}
\usepackage{caption}
%%% bibliography package
\usepackage[longnamesfirst,super]{natbib}
%%% settings
\setcitestyle{square}
\pagestyle{fancy}
\renewcommand{\chaptermark}[1]{\markboth{\thechapter .\ #1}{}}
\renewcommand{\sectionmark}[1]{\markright{\thesection .\ #1}{}}
\fancyhf{} % clear all fields
\fancyhead[LE]{\sffamily\leftmark}
\fancyhead[RO]{\sffamily \rightmark}
\fancyfoot[LE,RO]{\thepage}
\renewcommand{\headrulewidth}{0.0pt}
\renewcommand{\baselinestretch}{1.25}
\setlength{\headheight}{14.5pt}
\captionsetup{font={small,sf}}
\setlength{\parindent}{1cm} %%% WHY?
\begin{document}
\begin{figure}
\centering
\fbox{\includegraphics[scale=0.150,trim=300 450 300 500,clip]{imagefilename.eps}}
\caption{This text is the image caption for the image showed. Note that this text
is too separated from the image above.}
\label{image}
\end{figure}
\end{document}
The packages times and epsfig are obsolete; the second one should never be used, to substitute the first one load mathptmx or, better
\usepackage{newtxtext,newtxmath}
The option dvips should never be passed to graphicx.
For changing the font of captions, use the caption package. Don't put figure inside a center environment and don't use center inside, but the simple declaration \centering.
Best Answer
After a few hours of trial and error it turns out that a package setting for a different package was causing the problem in graphicx. I was using a template given to me by someone else which had:
defined. Alas, the
dvipsoption was causing the problem. Removing it I am now able to include a .png with\includegraphicsand set the size with the thewidthoption.