Why can't pdflatex print EPS figures?

EPS is more than an image format: it's an entire programming language. The way that DVI mode includes EPS images is to simply leave a space for them in the output. If you look at a DVI, you'll find that the EPS images are not actually added to it: they have to be present for appropriate interpretation when looking at the DVI. When you convert the DVI to EPS format (or directly to PDF), it is the conversion tool that deals with the EPS, not TeX at all. (The usual DVI route uses GhostScript: it does contain all of the code to interpret EPS files.)

When producing a PDF directly, the images do have to be properly included by pdfTeX. It doesn't include an EPS interpreter (which would be much too complex to do), and instead expects that some other tool (probably GhostScript) is used first to make PDF files for inclusion. PDF files use some of the same concepts as EPS, but in a way that pdfTeX can use successfully.

Yes it can and it will be default in TeXLive2010.

You need:

1. \usepackage{epstopdf} in the preemble
2. Include graphics without extension e.g \includegraphics{picture}
3. pdflatex -shell-escape or enabling write18 on windows

I am using TeXStudio 2.5.1 on Windows 7, and found I need to have the \usepackage{epstopdf} line after the line \usepackage{graphicx} in my preamble ... Not sure why it would matter, but it works.