In the movie, a hippie like person in the crowd of people watching the Martians land for the first time sent out a dove when the Martians "declared peace" and that set them off. They ended up vaporizing everyone in the crowd.
Among the people in the crowd was a reporter who carried her little mini Chihuahua around everywhere who almost made it out alive, but ended up getting taken by the Martians. They switched her head with her dogs head. Both of them are still very much alive but just "not themselves"
In the end, it turns out that the Martians cannot take loud obnoxious music and it makes their heads explode.
Tom Jones actually did make a guest appearance in Mars Attacks and at the end of the movie sang "It's Not Unusual"