Moderate to average, in comparison to many other breeds. They are not a lazy breed yet may occupy your couch for a day if left to do so. A dog that's been indoors for 8-hours awaiting its family's arrival from work will require more daily time for dog fitness. Your resting Dane will have more energy to burn than a dog who has had outdoor access during the day. Great Danes as a breed in general, do not need excessive exercise.
Over exercising a Great Dane, especially a growing puppy is not recommended. Many Dane owners actually try to minimize Great Dane activity as to just enough to stay healthy and in shape for the first 18-months or so. Over working your growing pup could have adverse affects on hip and joint development.
Daily walks are highly recommended and offer mental stimulation, socialization and fitness for your dog perfectly. A half hour, to 1-hour walk should be planned for, at least once a day. Interestingly, the pace that a human walks will only allow a Great Dane to slowly lumber along requiring a longer walk and more time. Jogging with a Dane will actually allow it to gait at a nice aerobic pace. A Dane who has courteous leash manner and does not pull or stop suddenly makes a perfect partner for a bicycle ride as well.
Back yard and outdoor time will also suffice, however, the benefits of a structured leash walk and many socialization opportunities will be lost. A minimum 6-foot high fence or electric containment fence is highly recommended should your Dane be left outdoors unattended.
Dog friendly parks, or places where dogs congregate are also great for large breed exercise and socialization. Emphasis should be given to Keeping a close watch when your Dane is running around with the pack. They tend to tire more quickly than many smaller breeds do to their massive frame and body weight. If you notice your dog begin to tire, slow the Great Dane activity and calm things down a bit.
For us, a good half hour of heavy running with the dog park pack and we call it a day. Great Danes have very long limbs, an exhausted Dane is prone to injury. Beyond that, daily games of fetch, a river swim, or evening walk keeps our boy trim, chiseled and healthy.
For the more athletically minded group, Great Danes due quite well, and are quite impressive while participating in different canine activities like lure coursing, agility, obedience competition, fly-ball and tracking.