Both my dogs are rescues. The Irish Terrier was given up at 10 months old because he was the husband's dog and the husband was now working in Abu Dhai or some such. The wife worked 12 hours shift work and had a 11 yr old son, but they just left the pup in the courtyard, never walking or training it ... and low and behold it started to BARK! At least she had the sense to contact Irish Terrier Rescue in the UK, but the lady she first talked to gave her such a yelling at she nearly didn't call back. The breeder, by the way, would have taken the dog back like a shot, but was never consulted until the rescue was a done deal. They were furious with just about everyone, but very nice to me as a new IT owner.
The cattle dog/Kelpie was given up at 8 yrs old because .... they were moving house. She came to me with an untreated, partially healed cruciate ligament tear. But she is an old dear, really. Good thing the boy IT is such a sook, she pushes him around something awful!
Most of the rescues I've participated in have been animals that were driven to a park or parking lot and pushed out of the car. God, I could happily do the same to those people. Why do they do it? Because they would have to pay a fee to turn it into a shelter.