A big problem is people not spaying/neutering their cats, letting them roam free and then the stray cat population just keeps growing.
Years ago, we had a beautiful, but very skittish cat that kept showing up to eat the bread we'd throw out for the birds. He was so skinny. And I saw one of the neighbors (JERK!) chasing the cat and trying to kick it, succeeding once. We started putting some cheap cat food out for him. He would run away if we tried to go outside with it. Eventually, he started living under our back deck and became somewhat more friendly. Then one very bitter, cold winter night he kept crying at our doorwall and licking his paws, which then would get stuck on the metal part. It was heartbreaking. I talked the hubby into letting him inside just for ONE night. Well, long story short, he stayed until he died many years later! He always seemed very grateful, like he knew we saved his life.