Well, dogs are basically lactose-intolerant. They haven't got the enzyme needed to properly digest milk and milk products.
This affects some dogs more than others.
Some will have diarrhea. If your dog has never had any symptoms like rom eating yogurt, then she is probably one of those dogs who can tolerate milk based foods better than other dogs.
But that still doesn't make it a great idea. Maybe a little, very occasionally, and make sure it's a plain yogurt. The sugars also won't be so good for her. And some may contain artificial sweeteners which are actually toxic for dogs. Xylitol, for example, can be actually deadly for them.
I agree with ginger899. My dog is the same way and she loves all things dairy and will always try to sneak some, I only give some to her occaisionaly and usually it's just a lick off my finger.