We've got one, and he is lovely. He's really laid back, will let kids do anything to him, and most of the time you hardly know he's there.
Ours is an ex-racer, so we've never had any accidents in the house, and he walks really well on a lead.
They're meant to form a loyalty to one person in particular, but ours just seems to be loyal to the last person that fed him
They don't need (contrary to the silly woman at the rescue centre!) hours of walks a day. 1 or 2 20 minute sprints is more than enough. If I can't get out with him, ours will just do super fast laps round the garden.
They look beautiful, and other greyhound / whippet owners will always stop and talk to you about them. I forget how gorgeous they are until I'm admiring somebody else's dog, and then realise that mine isn't much different!
Downsides - ours doesn't know how to play. Might be a one-off, but more likely because he wasn't taught as a puppy. Shame, because ds would love to throw sticks for him etc. Also, he is very unreliable off the lead, and would just run for miles if the mood took him. We only ever let him off the lead on long empty beaches. We were also told he should be muzzled at all times, and they wouldn't let us leave the rescue home without buying one. Half-way home he was hyper-ventilating, so I took it off, and he's never since worn it. OK, so he has tried to eat a few hedgehogs (won't learn), and would probably eat a cat if he caught one, but we don't let him off the lead usually, so it's not a real issue for us.
Ex-racers in particular have special dietary needs, ours can't tolerate rich food or dog meat, and is more than happy on the cheapest all-in-one dog food. Probably a benefit!
If the size of the dog worries you (we have a male, so they can be quite big, but ours is on the small size), whippets are a nice half-way house. My mum has one, and she is absolutely lovely, has all the great traits of our greyhound, and none of his disadvantages. I went looking for one when I got our dog, but there weren't any, hence we came home with him!