Seconded. They are actually great dogs for apartments or condos. Danes are big, lazy, friendly dogs who aren't especially bright but are very easy to live with. They WILL take over a sofa for their bed but they aren't going to require nearly as much exercise as a Lab, will mature at a younger age and will be much quieter. They don't actually eat a huge amount, like everyone assumes; our female Dane eats 2 cups in the morning and 2 cups of dry food at night.
Downside is that they have shorter lifespans (8-10 years) and unless you really work hard they'll probably just learn basic commands, no fancy tricks.
Adopt an adult from a rescue; lots of people have given up perfectly good Danes recently because of the economy. They move into an apartment with a size limit and their dog has to go.

Adopting a rescue means that you will also skip past the puppy stage and not have to worry about housebreaking or chewed slippers.
They're a wonderful breed with tons of love to give.