To no one in particular:
I always thought that Greyhounds need lots of exercise/love to run and that Bassett Hounds are by far the laziest dogs.
Trained them and owned them for 13 years. To race them, yes, they need regular exercise. To keep any of the muscle tone from the track you will need to provide exercise. If that is not important to you they really don't need anything.
Yes they love to RACE, not necessarily run alone. They love to kill the neighbors cat too, so breaking one of the kill instinct can be a long road if you intend to ever let one off the lead. Most are dominant in nature, so issues with other dogs can be a problem, especially for the other dog if it thinks it can challenge one to a fight. A greyhound would tear a pitbull a new one in nanoseconds.
In a home sitting, they will take up a spot on the couch and leave only when required. They were treated as royalty for centuries and expected to do no work other than race, and expect to be treated as such. They do make wonderful pets if you have time to spend re-training them. Another note, there are many that smile. Not some faint hint at a smile, a complete smile when truly happy at a situation.
Pound dogs are great if you find the right one for your situation. As someone else said, they know and will love you forever. Keep in mind they are not likely to be free, most places now require around $75 for the effort. They have to find money somewhere.
Questions that you should consider before deciding, and I definitely am in the "get a dog" camp:
Apartment or home?
Fence or no?
An area to walk them if no fence?
Ability to take them out before work, after, and before bed?
etc....
Cats suck by the way (compared to a dog).