Boy, I leave for a couple of days, and things get all interesting around here.
Lots of thoughts to the many different directions this thread has gone:
1) OP: First, it depends on how experienced you are with dogs, but my advice from lots of years training and working with them, as well as daily experience running with my two (used to be two Great Danes, now a Great Dane and a 100# Husky/Malamute mix): If you're walking your dogs, don't let them be out in front of you--you're the leader, you lead. When you get charged by an off-leash dog, you step in front, and face the charging dog, and give a strong "No." Not screaming, not high-pitched, not aggressive, just authoritative. 99% of the time, they'll stop or turn off and try to get around you. They're not coming after you, they're charging the dog; once they realize that you're together and they're outnumbered, they don't want a fight. You taking charge and establishing yourself as boss will resolve this without any problems in almost every situation. If you're dogs get out front, you have a lot higher chance of a dog fight, which is when it sounds like you got bit. On that 1% chance that it's not, remember that you're an adult human being who weighs at least twice as much, and are stronger. You can easily defend yourself against a dog, but like I said earlier, it's likely to never happen. You got it right in one of your later comments: any kind of spray, taser, or handgun in close quarters with two other dogs on leashes is probably going to turn out bad.
2) Great Danes are incredibly friendly dogs away from the house--I've raised Danes my whole life, and showed them growing up, and have only met one Dane that some idiot tried to make viscous. They are also some of the best natural protection dogs I've ever seen. If I'm home and let you in, you're a welcome guest who will learn that no dog is too big to be a lap dog. If you come to the door, and I don't let you in, you'll be watched like a hawk. When my daughter was younger her best buddy was a 140# male who watched over her like a hawk. The neighbors in our circle laughed at the little 4 year old girl walking her dog with her arm extended over her head to reach his collar. He'd sleep in the yard and watch her play, and if a stranger came into the street, he'd walk to the edge of the yard, and do his best Hulk Hogan flex. He knew when to be protective. Any other times, he was the biggest, friendliest doof you'd ever meet.
3) To all the comments about AJBert's posts: How about we all back off the rhetoric a little since we don't know all the details? If you come in my house when no one's home, you can bet your rear you're going to get bit... you're liable to be hospitalized. My dogs are not vicious; quite the opposite, I've never had anyone NOT comment on how well-trained my dogs are. But protecting their property is part of their job. Are you saying you think the dog should be put down because an intruder got bit?
4) As to the discussion of the best breed: I'll put in a vote for Great Dane, but not for any Northern breed. The one I've got now is the only one I'll ever have. Stubborn, flaky, extremely pack-oriented, and either very dominant or very submissive. I don't think I've met any that are "balanced". Kenai is as close to a wolf personality as I've ever seen... He's a one-person dog, and I'm it. Anyone else, he'll try to dominate. But, he's part of the family, so he gets to stay. But there won't be another one.