Sandy,
It helps to know your neighbor. We have one we help and have asked first. She's OK with it because she has no tools and is never home. Our other neighbor, we go into their back yard, across the alley to pick up walnuts that fell off our tree. To fix the worst of that, we cut the branches off that over hang, but they still fall and bounce. She's OK with that, She's a widow and we've grown up with her kids.
I am possessive of my yard too, but will allow some things. Third neighbor has good kids. Their ball rolls into my yard, they stay on the paths and carefully retrieve it. If it goes in the flower bed they leave it. I'll toss it back later.
I guess I live in a pretty good spot :o)