There are a couple of things at work, and neither of them are
filters.

       In "Saving Private Ryan", the film was intentionally, and digitally,
reduced in saturation in order to achieve the effect. Not hard to do with a
digital file (scanned film or image from digital camera), but it requires
post-processing with an editing program like Photoshop or Paint Shop Pro.
While there are film types that have a reduced saturation and lower
contrast, they do not come anywhere near this extent.

       The "grittiness" is best referred to as grain, and this is a trait of
the emulsion. Again, no films feature this to such an extent, but it's
possible to produce this both digitally and by special processing.

       In order to increase grain without digital editing, the film has to
be shot at a much higher ISO than rated, which is essentially
underexposure. Then it has to be processed to account for this - the whole
procedure is called "pushing" and is usually done in increments of f-stops,
one stop being the doubling of the rated ISO.

       The problem with this is, it increases the contrast at the same time,
which is the opposite direction from what you're after with the color
saturation, though it may produce the shadow effects you want.

       You can reduce saturation in a film by "pulling" it, the opposite of
the above. You shoot it at a *lower* ISO than rated and process accordingly
- this washes out the color a little bit, lowering contrast. But this means
the shadows won't be deep, they'll be more grey.

       So, to really mimic the effect, you're into handling the images
digitally, reducing saturation while keeping the contrast in place, or
perhaps increasing it slightly, then adding grain or noise to get the
gritty feel.

       Unless you could get your hands on some of the first color films that
were introduced. They should replicate the effect fairly well (which is
what Spielberg was trying to do). Methinks this would be hard to find,
though ;-)

       Good luck,

    - Al.