If you look at the greyhound's large frame, you might be tempted to think of making one a guard dog. Greyhounds do not make a good guard dog. Despite the fact that they look large and intimidating, they are actually very docile creatures. They can spook easily and are more likely to run and hide when faced with an intruder than to attack.
Another interesting feature of a greyhound that doesn't fit with the ideal of a guard dog, is that the bark has pretty much been bred out of the breed. This was to keep them from being very noisy in their crates as they were carted from race to race. So now, the greyhound isn't as noisy as a guard dog and would probably not even bother to bark if someone crossed into your territory.
Greyhounds come in a range of temperaments. You can get one that is very skittish or one that loves to lie around the couch a lot. You might even get one that behaves both ways, depending on the situation. One thing is for sure; even with obedience training the dog's attention is so easily distracted by anything flitting in its proximity that your commands are sometimes ignored. This isn't so much because the dog is strong-willed; it is because there are just so many fascinating things to chase nearby.
While a greyhound may be willing to horse around with your children, another pet in the house can be too irresistible for it's predatory instincts. It may end up chasing your cat around the house and hurting it if you have one. It certainly won't act like a sheep-herding breed or a guard dog breed that considers every part of your property to be sacred and worth guarding. You may even see greyhounds put behind large privacy fences and that might make you think they are aggressive dogs. Mostly, the privacy fence is to keep them from chasing the neighbor's cats and other small creatures.
The greyhound is so timid that it may even be hard at first to get it out of its shell. You will have to spend a great deal of time socializing it as a pup to make it friendly. If it is attacked, the greyhound will usually freeze or become very startled. It isn't aggressive enough to thwart an attacker or even intimidate it with a bark, since it doesn't really have one. It is not a stoic breed and instead can easily stressed or emotionally upset when its daily routine is changed. While the many docile traits do not make it a good candidate as a guard dog, it does make it a great candidate as a family dog. It can be very loyal, very loving, and quite friendly when socialized enough as a puppy.