Why would my dog attack my other dog for no reason?

Actually, there is a reason, you just haven't figured it out yet. Dogs don't attack other dogs for "no reason".

The staring was the first sign that something was going to go down. Staring is a "challenging" behavior.

It could be that the younger dog wants to be alpha and is looking to rise in her pack position. Though the dogs get along 95% of the time, I would not allow them to be together unsupervised. If your not home, then the young dog should be crated.

I found a little female dog about a year and a half ago either lost or abandoned on my street. She was about 7 months old at the time. We decided to keep her. I already have two older male dogs that are about 12 years old. They all seem to get along well, until for no obvious reason, she attacks one of the males. It's so horrible when this happens. The older dog doesn't fight back and this female savagely rips at his skin and I'm sure if I didn't pull them apart, she wouldn't stop until he was dead. She has left large open flesh wounds on him. I don't know what to do. Any other time she is as sweet as she can be, loves people and is very playful with the other dog. A couple incidences were as someone just came to the door and she just turned and went crazy on him. I don't know what to do. Everyone says I should get rid of her, but it's so hard. Any advise would be greatly appreciated...

If they are both males, the younger/smaller dog is challenging the older dog for the alpha dog position. The younger dog is testing the water to see if he can challenge the older dog. The younger dog didn't attack you because they already understand you are the pack leader. You will need to reinforce to the younger dog that the older dog is the alpha by feeding, brushing, putting the leash on for a walk for the older dog first and make him wait his turn. Also if the terrier mix hasn't been neutered I recommend doing so. If she is willing to attack the older dog, I would not trust the younger dog around small children. This doesn't sound like the typical attempt to get the older dog to play as she did do physical damage to the older dog. Staring is considered rude as a general rule with dogs. Glad to hear the older dog didn't react to the challenge.

Dogs can get possessive. He just didn't want the other dog to be able to take away the toy and was telling the other dog that!

Sounds like tension. Make sure that you prevent situations. They need to work on their relationship. Make sure they are both fixed. Take them for walks together, and do not over please one than the other. Work on training with them. Sometimes the littlest things can trigger a fight, but after a fight does happen I have two pitbulls who cuddle together and sleep together, but one day they fought, and I corrected the behavior and they have not fought since. After the fight I put them in their huge kennel together to get the bond back up and then took them for a walk together. You need to keep your eye on them all the time. Dogs are tricky.