Use the epstopdf program.
However, if you used the method suggested above (including PNG-images into your EPS figures), you will most likely be disappointed by the result. The problem is that most programs that convert EPS to PDF will use a lossy encryption (like JPEG) for bitmaps, and with a rather dodgy quality setting as well! This can be particularly annoying if you submit a nice EPS figure with your LaTeX code to a publisher, and the finished PDF file, or even the printed version, ends up looking dodgy.
However, PDF does support lossless image compression (via Flate); the question is how to make sure your converted EPS file uses it? The best solution seems to be, as suggested by Gary Steele to include the following code directly in your PostScript file.
systemdict /setdistillerparams known {
<< /AutoFilterColorImages false /ColorImageFilter /FlateEncode >> setdistillerparams
} if
systemdict /setdistillerparams known {
<< /AutoFilterGrayImages false /GrayImageFilter /FlateEncode >> setdistillerparams
} if
This tells your conversion program to use Flate both for color and for
grayscale images. An advantage of this method is that *any* conversion
utility which conforms to Adobe's standard should now obey these
rules
(e.g. if you submit your files to the ArXiV
and want to create a PDF file.
It also should be possible to force the same settings using the GS_OPTIONS environment variable. I haven't tested this; in particular, I don't know if it will work for GhostScript under MS Windows.
Suppose you have a figure in your paper illustrating the proof of your theorem, a fundamental construction, etc. etc. It is likely that you want to label some of the objects in the figure with the names they are given in your text. If you create your figures with a standard graphics program, then it is likely that the font used to render these names is different from the LaTeX fonts in the rest of your article, not to mention the fact that some of the more esoteric LaTeX symbols may not even be available to you.
The solution is to produce LateX code which will position your symbols over the included EPS figure. But would you really want to do this by hand?
The most convenient way to do this today is to use the SVG file format, together with the Inkscape program. Previously I used the FIG format and XFig program (see below), but the advantage of SVG is that it is an open format (today e.g. supported by most web-browsers). It is a standard format today, and there are many free SVG files available that may have elements that you can re-use in your own figures. However, always make sure to check the copyright and attribution requirements before using somebody else's work!
How to use SVG to create LaTeX figures is explained well in this document on Inkscape and LaTeX.
To use the FIG/XFig solution, produce a .fig-file of your figure (e.g. using xfig or similar programs, or writing the xfig-code directly from whatever program is making your calculations) and use the fig2dev program with output formats pstex and pstex_t to produce both an EPS-file and a file containing LaTeX-code.