Dobermans are wonderful, but they can definitely be trying sometimes. I love my Dobermans whole heartedly and would not trade them for the world, but at the same time, I do sometimes complain about them as well!
Mine were what I'd consider to be very high energy until they matured around 2-2 1/2 years old. Now I would consider them moderate-high energy. I think the biggest thing, much like what Grace said in a recent Border Collie thread, is to
not over stimulate and keep them busy constantly, otherwise they're going to crave non-stop exercise and attention and not know how to settle. I made this mistake with Keira as a puppy, as I figured the more exercise I gave her = the more tired she'd be, & the happier I'd be. Boy, how wrong I was! The more exercise I gave her = the more stamina she gained and the less relaxed and focused she became. She was my first Doberman puppy, and the most high energy dog I've ever raised and we all make mistakes and learn. With Ripley, I gave him just the amount of exercise he needed & did not make a huge attempt to exhaust him. He was instead rewarded for calm behaviour (settling on his own, going to his bed, chewing bones, etc.), and as a result, was a much more relaxed, easy to live with puppy than Keira was. Mine needed a good 45min run/romp at the park every couple of days, and every day I would play with them for about the same amount of time in the yard or I would let them wrestle and chase eachother. Mental stimulation is even more important to my dogs, especially as youngsters, and I tried to work with them a few times a day at short intervals every day. Now that they're adults, they don't need that much. They could still do it and be happy, but now they're content to sleep most of the day or chew a bone or something, and are good with their weekly run at the park and some outside playtime in the backyard + I still work on training a few times a week as well. They don't crave stimulation and exercise like they used to. They're happy when they get it, and if they don't, they're fine. But I definitely try not to go too many days in a row without doing anything with them (happens sometimes in the winter when it's 40 below). Then they start getting a little stir crazy. I find the girls lose a lot of their playfulness by the time they hit maturity, but the boys tend to think they're puppies for life (not all of them of course). Keira will play a bit, but she's not into it anymore like she used to be, whereas Ripley would love if I could just stay home and play with him all day. He likes to be chased, he likes fetch, he loves tug, etc. And he's always up for play with other dogs, too. Where as Keira really couldn't care less after a few minutes... that is if she even bothers at all. She'd rather do her own thing and run aimlessly than bounce around too much or fetch a ball, unless she's in a particular mood. Which can make her hard to exercise, as she's still full of energy, but she just doesn't really want to play -- she just wants to run. This seems like a pretty typical trait between the two genders. Boys are much more clownish and goofy a lot of times, and girls are generally much more serious.
Dobermans are very versatile. Mine are up for most things asked of them, but just beware that swimming might not be one of them! Ripley can't swim for the life of him (need to get him a life jacket and teach him properly), but attempts it, and Keira thinks she might very well melt. Mine will both go into the water up to a certain point, but they have to be able to touch the ground. That said, some people on the Doberman board I belong to (the one Fran linked to) have had better luck with swimming Dobes! Other than that, mine are game for virtually anything. Just beware that during colder temperatures if you're out hiking or camping or something that they might need to wear a coat. They're about as tolerant of the weather as we humans are with their single coat.
Dobermans are an odd mix of sensitive but headstrong at the same time. Much more so than any other breed I've owned or have had experience training. They need a firm, consistent handler, but not one who will use excessive force. Most that I know do not do well with anger (ie: yelling or just feeling really mad/frustrated) -- be it directed toward them or otherwise. I've seen more than one cower and tremble over a human's anger, and these are dogs who are otherwise what I would call very stable and virtually bombproof in the majority of other situations.
I personally don't find them super easy to train. I don't find them really that difficult either... but definitely not as easy as Dance is, or even as easy as my Rottweilers were. They're incredibly intelligent, they are thinkers, and they do like to work and learn. However, many can be very easily distracted/unfocused and not always very people pleasing. In that, I mean that they certainly don't want to upset you, but they don't always go out of their way to please you either. I think focus (in my experience) is the biggest key when it comes to training a Doberman, though. Once the dog has good focus, it is pretty easy to get them to do almost anything. It's just getting that focus sometimes that can be very challenging.
Dog reactivity seems to be big in this breed. I've known a lot of very leash and/or just simply dog reactive Dobermans, and despite all of the training and socialization that Ripley has had, even he has some minor reactivity unfortunately (on leash, caused by being unsure of and frustrated by not being able to meet another dog). Dog aggression is another common issue in the breed, but mostly in the way of Same Sex Aggression. This is prevalent in both sexes, but it is more common in males and is recommended not to ever have a male Doberman living permanently in the same household with another male dog ever. It is not as common in females, but when it does happen, it is often even more dangerous and intense. So beware and make sure you match the right dog to your household.
All of the Dobermans I know are very trusting and compliant. I can do absolutely anything I want to do to my dogs without an issue. They take whatever I throw at them in stride and just trust that if I'm (or another person) doing something they don't like, it must be for a reason, otherwise I wouldn't be doing it. So they just take it without fidgeting or complaining or anything.
They are very, very people oriented. This is a breed bred for years as a personal protection dog, and so as a result, they are naturally very attached to their people. I think they take it a step further than "velcro"... they're more like glue. If they had it their way, mine would have some part of their body touching me at all times, and eyes on me at every single second of the day. Separation anxiety can be a problem if you give in to their (often excessive) neediness, but I personally have not had an SA issues with the four I've had in our home. They can be pushy and rude when it comes to attention as well (headbutting, laying on you, leaning hard into you, screeching for dinner, moaning and whining for attention, etc.), so make sure you stay on top of that and don't let a Doberman get away with all of that stuff. They definitely choose one person as their person in a family, but they do love their family as a whole as well.
They can be pretty vocal in the way of whines and moans and groans go, and they have a scream that could put most dogs to shame if they're really adamantly demanding something. But mostly I find them pretty quiet, and they don't bark needlessly either. I find males to be more protective of their property as well as their people, and will bark more at different noises and such surrounding the house without thinking first, where as females in my experience are a little more focused on just their people and a little bit less on property, and they think and assess a tad more before they bark at something... to see if it really could be a threat or not. I'm not sure if that's true for all Dobermans, but it is for all of the ones I know, including my own.
Health issues do run pretty rampant in the breed. There is Dilated Cardiomyopathy (which is in every single line -- you can try your best to avoid DCM, but there is always a chance your dog might end up with it), wobblers, different cancers, thyroid, hip displaysia, vwd etc. If you are not adopting from rescue, make absolutely sure whichever breeder you go to has had health testing done on their dogs.
I have known a lot of "problem" Dobermans as far as rude behaviour (jumping, incessant barking), OCD behaviours, unable to settle, etc. but most of it stems from a lack of leadership and know how. And also, a lot of them are very poorly bred and poorly socialized as well which does not help. I think that a lot of people end up with Dobermans because they're pretty, and don't realize just how much dog they are. They are not easy by any means, and require more work and time than any other breed I've ever had, but they are wonderful for the right owner/somebody who has dog knowledge and is willing to learn.
Oh, and as an aside, Dobermans are not considered a "Bully" breed. They do recieve the same sort of scrutiny however.
I am sure there is a lot more I could add, but those are the main things I can think of at the moment. And other Doberman owners around here might have had different experiences with the breed, so hopefully they'll chime in as well.