The straps are probably the best bit. You should be able to reassemble them into a short luggage strap perhaps to use with panniers or a rucksack.
If any removable pads have survived wear and tear up to now, they might fit your replacement, and a spare set of pads is a good thing for when the other pads are destinking (mine need a periodic soak in bleach).
I keep an old (but not visibly damaged) helmet under my desk in work, because I also keep a bike near work and in theory could end up wanting to use it and not having my current helmet.
The shape and size are too awkward for many potential uses - while you could probably make one into a lunch bag or something it would take more materials than it's worth. I wondered about keeping it as a jig or stand foe use when tinkering with helmet-mounted lights or cameras (something I do more than most people) but helmets are all different and what mounts securely on one won't necessarily work on another.
You may have recycling for the foam in your area if you can get the outer shell off.