You are probably not actually compiling using LaTeX, but more likely you are using pdfLaTeX, which is much more commonly used these days to create PDF's directly from the .tex files. True LaTeX (like TeX that it is based on) creates .dvi files, not PDF's.
This difference is important as the different compilation engines support different image formats. The best way is to check the documentation for the exact compilation engine that you are using. In the case of pdfLaTeX compilation (the most popular today), EPS files are not supported.
The WikiBooks website is a good source of info on LaTeX:
In particular, it says this:
Compiling with latex
- The only format you can include while compiling with latex is Encapsulated PostScript (EPS).
Compiling with pdflatex
If you are compiling with pdflatex to produce a PDF, you have a wider choice. You can insert:
- JPG, widely used on Internet, digital cameras, etc. They are the best choice if you want to insert photos.
- PNG, a very common format (even if not as much as JPG); it's a lossless format and it's the best choice for diagrams (if you were not able to generate a vector version) and screenshots.
- PDF, it is widely used for documents but can be used to store images as well. It supports both vector and bit-map images, but it's not recommended for the latter, as JPG or PNG will provide the same result using less disk space.
It goes on to give state that you can use EPS with pdfLaTeX, but only with the help of some other tools or some intermediate processing
- EPS can be used with the help of the epstopdf package.
The WikiBooks website will give a good intro on how to do this.