The Great Danes I have known have all been goofy, sweet and gentle, and horrendously expensive to feed. My parents used to use a dishpan as a food bowl. They also take over the entire couch or the entire bed if you let them and can easily remove dinner from the table with one swipe of the tongue.
As others have said, they tend to have hip problems due to size and poor breeding practices, and like other large dogs, they are not known to live terribly long. Because of their size it is very, very important that you train them to not be aggressive and to regard you as the leader of the pack.
Good pets, yes, but then most dogs are good pets if you are a good owner.