There are several vector graphics format in use these days by vector graphics packages, the most common ones being pdf, eps, and svg.
SVG tends to be the de facto internal working format for most of them these days, and it is a very good format for web applications as most browser will be able to display them natively. However, unfortunately, svg is currently not supported in LaTeX documents.
The historical format for vector graphics in TeX is eps and it is indeed the only format supported by the original latex, even for raster based images (indeed, all these file formats can contain both vector and raster based images).
With the graphicx package, and pdflatex (and newer incarnations such as xelatex and lualatex) you can now include raster files such as jpg, png, and so on, without having to put them in a eps container, and you can also include pdf files, however you lose the ability to include eps files.
Most graphics packages will allow you to export as eps or pdf so you can choose at the time which format you want. Alternatively, you can easily convert from one format to the other with command line tools such as epstopdf.
As for which format is better, this is open for debate, pdf is basically built on eps with more features such as embed fonts, including ttf and otf ones, and compressibility (so a pdf will usually be smaller than an eps) among others. People will usually also have something installed on there computer that reads pdf, whereas, eps may be an issue.
Best Answer
EPS (PostScript) itself cannot show transparencies. But it is no problem to convert an EPS image to PDF (which will already be the default) before printing such a document. Log speech short sense: Use eps or pdf images and create a PDF document and everything will be fine.
\usepackage{epstopdf}will convert EPS images on-the-fly