Entitled neighbor digs a creek through his neighbor's backyard while they were on vacation, after they previously rejected the idea: 'Our fence is broken, but he says he will fix it and pay for it.'

You can't always control what your neighbor does. If you live in a neighborhood with a Homeowners' Association, you can absolutely control the color of mulch that your neighbor uses in their front lawn by reporting the issue to the HOA. But sometimes a neighbor will do whatever they want, whether an HOA is dictating their actions or not. 

It can be frustrating when one of your neighbors never mows their lawn, while you keep your lawn clean and pristine. While it doesn't technically harm you in any real way, it can reflect poorly on the neighborhood, dragging down property values and whatnot. And sometimes it's just an eyesore. People don't want to live next door to a house that is never maintained and looks shabby compared with the rest of the neighborhood, and that's why Homeowners Associations are desirable to some. 

There's a significant distinction between a neighbor neglecting to maintain their home and causing property damage to your home. If they paint their fence purple, they will probably be told by the city or the HOA to remove it, but if they paint your fence purple without your permission, that might be cause for filing a police report or suing for property damage.