Just to clarify the point made about greyhounds upthread. The reason so many of them turn up in rescue is nothing to do with them as individual dogs, it's because the racing industry spits out about 10,000 dogs a year, that are no longer needed for racing; so pounds, or a bolt gun or a rescue if they are lucky is their destination.
I do a lot of training with our four dogs - 3 greys and a lurcher. I've seen staffs do their GC Gold awards and I regularly see them competing in obedience and Rally (a form of obedience) events, very successfully.
In pretty much every basic obedience class I go to, the family that is towed in by a wrecking ball of a dog which then proceeds to trash the hall invariably owns a Labrador. They are absolute thugs (exceptions made for gundogs which are usually properly trained) but because of their lovely reputation as nice, middle class family pets people just smile indulgently.
Getting a well behaved, well trained dog (irrespective of breed) takes time and effort and a lot of practice. You only have to visit any park to see owners of all breeds with dogs pulling on the lead, jumping up at people or having zero recall. Or, if they don't let them off, the dog is on a horrible extending lead, having its neck jerked, and tripping up other park users.
A huge number of dogs of all breeds end up in rescue in their teenage years because they have outgrown the cute pup stage and owners simply can't be arsed to persevere with the time commitment of training. It's simply quicker and easier to send the dog to a rescue. 
Our dogs walk nicely on the lead, are carefully socialised, do controlled greetings, and respond nicely to basic commands - that didn't happen by accident. For our newest dog, she's currently doing 2 hours a week of formal classes (one basic obedience plus she's just starting Rally)plus practice at home each day of training split into 3 or 4 ten minute chunks, plus training built into her walks (e.g. reinforcing recall and loose lead walking). As a consequence, whenever we take her anywhere, we are congratulated on having a well mannered,delightful companion. She's a dream to work with, but the time commitment is not be underestimated to get any dog to this standard. I think the more general point to be made is that dog ownership of any breed is often undertaken far too lightly.