I adopted my greyhound 9 years ago. I was influenced in my decision by my sister, who had owned one for several years. They are a unique breed! Greyhounds, that is. Sisters are a whole other story...
One thing that must be said at the outset: Greyhounds are as affectionate as any dog on the planet. However, they are not always demonstrative in the usual "doggy" way of climbing all over you and soaking you with their spittle. They do indulge in this behavior to some limited extent, but usually only when you've arrived home after an absence of anywhere from 1 minute to 3 years. After a few moments of unreserved affection, they will revert to their regular state of quiet laziness.
Like all dogs, greyhounds beg for things like food and affection. However, their method makes their desires mildly inscrutable. They just stare at you until you can figure out what they want, like a Greenie, a Frosty Paws (aka crack for dogs), a rearranged bed, move your damned feet, pet me now!, please turn off the vacuum, brush my teeth, etc.
In the exercise department, they are the perfect apartment dog. They sleep approximately 23.5 hours out of every 24, with the remaining half hour being taken up with needs described in the previous paragraph.
In public, they tend to be very sweet and social dogs. But their behavior can sometimes be very aloof toward other dogs. They'll start off saying "hi" and check out the anal scent glands (the doggie version of reading their resume), but then quickly lose interest and start smelling a particularly attractive blade of grass that may have suddenly intruded itself upon their consciousness. That blade of grass can occupy their entire world for the next three or four minutes. At which point they will pee on it.
In terms of food, greyhounds can sometimes be very pernickety. They'll eat pretty much any treat that is offered, especially Greenies and Frosty Paws, and be enormously grateful for it afterwards, always coming back to you and thanking you for it by allowing you to pet them. They will also happily eat whatever you may have on your dinner plate, particularly if it's not good for them. However, their attitude toward kibble, the recommended foodstuff, is ambivalence. When no one is looking, they will eat it, but they seem to regard eating it as a surrender of some sort, and will avoid it until you are elsewhere, thereby retaining their plausible deniability (it was that Chihuahua from downstairs that ate it! I'm just famished, and should really have that Filet Mignon with Cabernet sauce!).
The grace and beauty of the greyhound is undeniable. To see a greyhound run is truly a life-altering experience. It's one thing to see it on a track (something which is thankfully becoming slightly more rare these days, although not rare enough), but it is quite another to see it heading straight at you, hellbent on that treat in your hand. They stop on a dime, and then look around nonchalantly. There is a video on YouTube from the show "Top Gear" showing a greyhound racing against a Mazda MX-5 (this site won't allow links, so paste "watch?v=zgG-n_KTZJM" after the last slash in the YouTube URL). The greyhound wins. According to this video, they are the second-fastest accelerating animal on earth, going from 0 to 45 in three strides (only the cheetah accelerates more quickly).
In my experience, there isn't an animal that is more rewarding to own, or be owned by, than a greyhound. They are loyal, loving, mild, sweet, and as unobtrusive as a 70 pound cat-in-a-deer's body can be. Supposedly, Alexander the Great loved his greyhound so much that he named a town after it. Someday I hope to do the same for mine.