Hmmmm, maybe they have relaxed it again - this was August 2011. We were told you absolutely cannot turn up on the day because they require everyone's passport details in advance - so it's minimum the day before, but realistically a few days during the summer. It was due to a terrorist threat...
Just in case this has passed you by - they have changed the rules about the Reichstag building in the last year, but most guidebooks haven't updated it yet.
You have to book online AT LEAST a few days before you want to go up into the dome. We turned up on the day (as our guidebook said to) and...