You could do it with an action in Photoshop (this is what I did with that Smash Bros.3DS file which was originally saved as nothing but two-page spreads) but there are a couple of caveats:
1. You would essentially be setting an action to do what you need to one page, and then automatically applying it to all other pages. This would basically require you to crop out one page, save, uncrop, crop out the other page, and save. The problem comes with the filenames when saving the split images. So far as I know, there's no way to set up an action to save files under different names than what the original file is, so if you opened up a jpg called "001" and tried the above method, it would save one half of the split as "001" and then save the other half as "001," copying over the first file. You could set the action to save one side in one folder and the other side in a separate folder, but then you'd still have two files named "001" and would have to rename all files in one of the folders, which could get really confusing.
In my opinion, the best you could do is set up two actions, one to crop the left side and one to crop the right. You'd need to do the saving manually, though, if you want to keep the filenames straight.
2. The above is only really applicable if the pages are all more or less the same size and the location of the split (or crop) is in the same place on every page, since the action would crop every page in the same place as wherever it was cropped when creating the action. Works like a charm on a digital rip where every page is identical, but might be less ideal on a scan.