Yup. It happens! I think it's caused by the nitrogen in the urine. There are a lot of dogs in my building and there are two spots where everyone takes their dogs to go potty--and you can definitely tell where they are.
If you're worried about the appearance of your lawn, I know my friend always tries to dilute out the spot where his dog just went pee with a watering can, and he says it helps.
That's right -- dog pee kills grass! But just like redrover said, if you wash down the area with a generous amount of water, you can avoid the grass die-off. Keep a bucket or hose handy.
I've always thought that if you have a dog, it's best not to care too much about the landscaping. The flowers in my flower beds are always in danger of being trampled by a chipmunk-hunting dog, but I've finally learned to put more flowers in big pots and set them around. Willie ignores them completely, and I get to have my flower fix.