I've had to deal with wild rodents in my garbage using violent (but less than lethal) means, but known house pets with collars or tags that belong to your neighbors? I mean, how much damage could a 7 pound cat possibly do to your property?

There is a cat that comes into our house through our cat flap and sprays. It also does this on our door step and all over our garden.

Eliminate all of the wildlife in the yard? Some people actually prefer a diverse array of wildlife over a neighbor's pet.

Seems passive aggressive to eliminate your neighbors pet. I'm not a social person, and I typically let me neighbors do as they please (as I want them to do with me) but if I have a problem with an animal I'll approach the owner.

If my neighbor kills my cat and makes my kids cry without talking to me about it first, I'm probably going to create problems for that neighbor that involve the local police department.

Probably not much. However if it was aggressive toward us or pissing on our patio furniture seats and did not appear to belong to anyone, that might be a different story. I'd actually probably just call animal control or trap it and release it somewhere far away.