Good points:
Cuddly
Loving
Gentle (mostly
)
Lazy
Elegant (usually)
Surprisingly trainable
Breathtaking at full speed
Fold up small
Lovely short, easy clean coats
Bad points:
Addictive
They think poking you with their very pointy noses is an acceptable form of communication
They steal your seat as soon as you stand up


They're wonderful little dogs. We got our first just over two years ago. Whippet number three is hopefully joining us late December/early January 
They can live with cats, especially if brought up with them from puppies but I wouldn't expect them to ever be trustworthy with cats that aren't "theirs".
They can be let off lead, both of ours go off lead for most of their walks. We keep them on lead around strange dogs (whippets, like most sighthounds, play in a way that isn't always appreciated by other types of dog) and anywhere near livestock. Their recall is great though, it's the single thing we put the most effort into when they're puppies and we constantly reinforce it.
Neither of ours have sensitive stomachs and none of their breeders' dogs do either. I think that's more an individual dog thing rather than a breed thing, at least in whippets.
They're not generally very barky (ours will sometimes alert bark if there's someone at the door but only really if they can be bothered
) but some can be quite whingey. One of ours is a whinger and will whine whenever he wants something or thinks something isn't quite right.
They need a surprisingly little exercise. Ours get between 30 and 60 minutes most days with a couple of longer walks each week. As long as they get a good run off lead they're more than happy with that and will snooze for the rest of the day. They hate rain and if it's raining really heavily we don't bother forcing them out as they'll mope along shivering regardless of how many layers they're wearing. Cold is acceptable as long as they're wrapped up nice and warm though we keep walks in the snow short as their feet get very cold.
As you can tell from little essay I'm a bit evangelical about whippets
Seriously though, fab little dogs and I honestly think they're ideal for such a wide range of people.