My boy did that for a few days. At first I gave in and gave him all sorts of things in his food bowl to get him to eat. Eventually, enough was enough. He wasn't getting any good food in his belly, just the fillers that I put in. (yogurt, cheese, etc.) I just stopped indulging him because all I was doing was making the problem worse. He had good kibble, nothing greasy or full of bad fillers, and it was tasty to him. He ate the other dogs food sometimes and it was the same thing! I just had enough, put his kibble down where he could get to it all day, and eventually he ate. Knock on wood, I haven't had a problem since then. He's turned into a huge beggar thanks to my mom and dad, but he won't go off his food in hopes of a tidbit. He'll eat his diner first then try to eat mine.
