1. Rick Steves Audio Europe (Free): So...Rick Steves is nothing new. If you go to any major tourist destination you'll see people toting around his books like a travel bible. But, he does make some really great podcasts, walking tours, and maps, all available in this app, which is completely free.
Listen to the podcasts to prepare for your trip, and then enjoy the guided walking tour on your MP3 player. I did this while traveling solo while in Paris, and Steves' app was a great way to learn about the city on my own time.
2. TripAdvisor Offline City Guides (Free): Again, Trip Advisor is nothing new to the travel industry. However, they have an amazing city guide app that was completely new to me. The beauty of this app is that once you have it all downloaded, it works fully without an internet connection (often hard to come by when abroad). You get full access to their reviews, suggested itineraries, self-guided tours, and best of all their maps. You can search by city, neighborhood, or near your current location. They even have a GPS-based 'Point Me There' feature, that works as a compass to guide you to your destination. Again, no internet needed, and it's all free.
I used this nonstop on my most recent trip to Europe and it made traveling so much easier. This app works for many cities in North America, South America, Europe, Asia & Pacific, and Middle East & Africa. Just make sure to download your desired city before you leave, just in case you don't have easy access to the internet.
(Images: TripAdvisor Screen Shots)