What is a good workflow for importing and cropping EPS images?

Firstly, the GIMP does appear to be an adequate and convenient tool for the job. EPS files seem to include a default resolution, which is what the GIMP displays when you open an EPS file, so don't change it:

Next, you can easily use your cursor to find one of two defining coordinates. In this example we do the top-left coordinate. You can see the approximate region of where the cursor is by the small box that is north-west of the figure. The coordinates are shown in the lower-left hand corner of the canvas window. Be sure to choose coordinates that TeX can work with (I don't think the default, px -- pixels, is supported in TeX; What are the possible dimensions / sizes / units LaTeX understands?). In our example we use millimeters (mm):

Now we can import it into a document. Again we will just test this coordinate for now:

documentclass{article}

usepackage[english]{babel}
usepackage{blindtext}

title{An EPS trimming workflow}
author{Brandon Barker}
date{today}

usepackage{caption}
usepackage{graphicx}
usepackage{subcaption}
usepackage{float}


begin{document}

% Let's draw a box around the figure so we
% can see where the figure's whitespace ends.
setlengthfboxsep{0pt}
setlengthfboxrule{1.5pt}

begin{figure}[h]
centering
% give some space for fbox:                    % l       b   r   t
fbox{includegraphics[width=0.9textwidth, trim=104.4mm 0mm 0mm 17.3mm, clip=true]
      {YeastExpFluxCompare}}
caption{blindtext}
label{fig:FluxExpCmp}
end{figure}

Please refer to Table~ref{fig:FluxExpCmp}.

end{document}

This results in the following output, showing that we have correctly made a close crop around the left and top edges of the figure.

You can use epspdftk, the gui interface to Siep Kroonenberg's epspdf.texlua script. It exists both for Windows and Linux and does everything (converting and cropping the resulting .pdf) in one step. I'll take the example of one of my old graphic files, produced with pstricks and pst-eps, that had a (very) badly computed bounding box. The procedure is very simple: launch epspdftk and check Compute tight bounding box, then click on Open to choose the file to be converted:

Once chosen, you may ask to view the .eps file:

Then click on Convert and save…. A second later, you can look at the resulting .pdf in your favourite pdf viewer:

The .texlua script can also be launched from the command line, if you want to do batch conversion.

I'm just adding this as a supplement to Werner's answer "B", which uses his method in a bash script that will process all eps files in specified directory:

#!/bin/bash

D=$1

# Process all EPS file in passed directory
for filename in $D/*.eps; do

    # Get path and filename without extension
    base=${filename%.*}

    # Convert EPS to PDF
    epstopdf "$base"".eps"

    # Crop PDF
    pdfcrop "$base"".pdf"

    # Convert PDF back to EPS
    pdftops -eps "$base""-crop.pdf" "$base"".eps"
done

# Remove the intermediate "crop" pdfs
rm $D/*-crop.pdf

The OP did not say whether the finished PDF document was intended for printing to paper, or for distribution in digital form.

If the purpose is printing to paper, then a vector image is not necessary, because the end user cannot zoom the image. In fact, a vector image may be undesirable, because vector images may contain ambiguous drawing instructions, which may be interpreted differently by different printers. If the printing is in commercial quantity, then vector images may be prohibited.

For paper, the best solution is usually to rasterize the EPS. GIMP can do the job, as can a few other programs. Ignore the "native" resolution of the EPS. Instead, think in terms of the physical printed size of the image (measured in inches) and the resolution (dots per inch). Unless your work is fine art, usually 300dpi suffices for color or grayscale images, 600dpi for black and white line art.

So, if your color image should be 4"W x 3"H, request 300dpi resolution when importing the EPS to GIMP. The rasterized image will be 1200 x 900 pixels. However, that is uncropped.

When you import, the dpi is specified, and the size is calculated. You can effectively change the size by changing the dpi at import. Then, use the Image Scale menu to change the dpi to 300, allowing the dimensions to follow.

Be sure to specify the resolution when you use includegraphics.