Your using pdfLaTeX, I suspect. First, remove the extension from your \includegraphics line. Then either switch to latex (dvi output) or include something like
I switched it to output a .dvi file instead of .pdf,
and the diagrams came out perfectly in my .dvi file, but then when I sent the .dvi file to someone by e-mail, the figures were gone.
Yes. The DVI file just contains pointers to the EPS information, which the viewer may or may not handle. You can either send the EPS files along with the DVI, or convert the DVI to PS and then to PDF, which will then be self-contained.