This apartment building near Munich, Germany, certainly defines high-density living. One smart way that its residents have made their balconies an extension of their private living space is by wrapping them in gridding, water-resistant fabric, or a mixture of both. This ensures that a little more of your private life stays private, even if you're nearly elbow to elbow with your next door neighbor.
In the Bay Area, I've seen friends use bamboo curtains, bright strips of fabric, or even woven saplings to create a privacy barrier on their decks, porches, or balconies. It's a great solution for making that space seem a little more personal and secure. Adding a table umbrella also helps to keep prying eyes from observing your business as well.
One of my favorite methods for adding a bit of privacy to a space like this is by using trellising plants. It requires a bit of patience, but if you live in a mild climate you can encourage morning glories, jasmine, passionflower, or other beautiful vines to slowly grow a privacy screen for you.
Have you added a privacy screen to your balcony? What did you make it from?