The thing about the iPhone that is a big difference from android and a big reason some people opt for android, is the inability to change out the default stock apps. Is there another photo album app to use? Sure! Will it replace the camera roll as the default photos app? NO. I think the camera roll is fine so I don't have a suggestion for you on this one so maybe someone can recommend an app.
One of my favorites that I get a lot of use from is Shazam. It is an app that if you hear a song on the radio or out somewhere and you want to know the name and artist, it will listen to the song for a few seconds and tell you who made it and what the name is.
If you are into Facebook or Twitter then there are dedicated apps for those as well.
Netflix has an app for streaming movies.
I use Moviefone to look up movie times but if you have an iPhone 4S or iPhone 5 then you can always ask Siri.
GoogleMaps now has there own dedicated app again so I would download that as well. I actually haven't had really any trouble with AppleMaps and think the app is pretty good but with Google's mapping data being so much superior since they have been at it for over a decade, it is always nice to have the other as a backup just incase AppleMaps might get something wrong. I also like to use Waze on road trips since it has notifications if a cop is checking speed of vehicles on the highway. It has a somewhat social media twist to it since users can input things like accidents, road work delays, cops presence, etc. You can even interact with other users.
You tube app is kind nice to have since it doesn't come stock anymore.
CSR Racing is a fun drag racing game.
Angry Birds is always a hit.
LockBox is good if you have a lot of passwords or other sensitive information that you need to keep up with but want to have a secured app to keep it in.
Pandora is great especially on road trips if your car has a hookup so you don't have to worry about listening to that same CD for 8 hours or hunting for radio stations.
Google Translate is great if you like to travel abroad or if you need to talk to someone who's first language is not english and their english is poor.
My speedometer used to be off and I used an app called Speedometer to figure out how bad it was and to verify the accuracy once I got the new speedo gear to correct it.
Those are just a few free apps that the average person might get some good use out of. Just hunt around the app store when you are bored and you should be able to find a lot of cool things. Not all apps are paid for so there are a lot of good free ones out there. Welcome to the iPhone family!