I first one I would recommend is an app called Starwalk. This app does cost $2.99 but well worth the money. Star Walk is an awesome augmented reality app. It tags stars, constellations, and satellites you point you iPhone at. I love this app because I know where the planets are and when you tap on an object it will give you awesome details. Star spotting is do fun.
The following apps are free and I would recommend due to their usefulness. Ok here we go... The Weather Channel, Quakes, iElements, Shazam, Project Noah, Fooducate, and WebMD are some I can think about.
When I look for an app I debate whether or not it will be useful in some way. Some apps will have a lite or free version which allows the end user to test it. If a user likes an app that was free to download then if the app is not too expensive then I would suggest paying for the upgrade. The cost is usually $0.99 to $2.99. The least to the most I will pay for an app.
Have a great day, my friend.