Can I not shovel my neighbours driveway so they have to do it?
Why are you not helping your neighbor out?
They would never do something nice for me, so why should I?
If that's the case, that makes sense and you should only worry about the area you're responsible for.  You shouldn't help out people who never help you out in return.  That would mean you're just being taken advantage of!
I want them to do something nice for me. They would never even say hi to me.
I don't think it is bad if you just take care of your own home. It's fine to only shovel the area that you're responsible for.  If you want to get on their good side maybe you could offer when you see them.