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You can use imagemagick's fuzz and blur to automatically crop / trim jpegs scans using jpegtran:

#/usr/bin/env bash
for f in ./*.jpg; do
	fuzzFactor=5
	box=$(convert "$f" -virtual-pixel edge -blur 0x15 -fuzz "$fuzzFactor"% -trim -format '%[fx:w]x%[fx:h]+%[fx:page.x]+%[fx:page.y]' info:)
	if [ $(echo $box | awk -F'[x+]' '{print (0+$3)+(0+$4)}') != 0 ]; then
		jpegtran -copy all -crop "$box" -outfile ${f%.jpg}_out.jpg "$f"
	fi
done

That is, imagemagick is used not to modify the files but to output the cropbox which is then passed to jpegtran to do the actual (semi-lossless) cropping. Imagemagick and jpegtran conveniently use the same geometry format to specify crop boxes so we only need to check there's actually something to cut (using awk to add the crop values to see if they sum greater than 0) before passing the box to jpegtran.

It's a very useful trick when going through scanned material.

Anyhow, the the fuzzFactor depends on saturation and often needs tweaking. i.e. 5% is what I personally found safe with unprocessed scans off desktop scanners. But, if lucky, you might get away with as much as 15% if the contrast between the blacks and whites really stands out. However, it's rarely the case...

Incidentally, jpegtran crop helper is nice.

p.s. This method was derived from a lossy method found in the imagemagick v6 docs.

I saw @nicolas-raoul post about partical JPEG recompression.
I think Jpegcoll is one of the solution for your requirement.
If you are interested in another lossless operations, you should check Betterjpeg.

Almost apps which have JPEG lossless operations are based on IJG code.
These apps are listed here.
But these apps have only rotate, flip and crop as lossless operation except above two probably.