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A regular need is a document to be distributed in more than one format: commonly both PostScript and PDF. The following advice is based on a post by one with much experience of dealing with the problem of dealing with EPS graphics in this case.

• Don’t specify a driver when loading loading whichever version of the graphics package you use. The scheme relies on the distribution’s ability to decide which driver is going to be used: the choice is between dvips and PDFTeX, in this case. Be sure to exclude options dvips, pdftex and dvipdfm (dvipdfm is not used in this scheme, but the aspirant PDF-maker may be using it for his output, before switching to the scheme).
• Use \includegraphics[...]{filename} without specifying the extension (i.e., neither .eps nor .pdf).
• For every .eps file you will be including, produce a .pdf version, as described in Graphics in PDFLaTeX. Having done this, you will have two copies of each graphic (a .eps and a .pdf file) in your directory.
• Use PDFLaTeX (rather than LaTeX–dvips–distillation or LaTeX–dvipdfm) to produce your PDF output.

Dvipdfm’s charms are less than attractive here: the document itself needs to be altered from its default (dvips) state, before dvipdfm will process it.