Games :
The Room 1 and 2
All final fantasies / Secret of Mana / Worms
Tengami
Eufloria HD
Star Command
NEW Orbit
F Sim space shuttle
Out There
Passage
All Readdle plugins (PDF expert / Documents (Document can only read), Scanner Pro etc)
Apple Pages/Number/Keynote (they are free the first months after phone purchase I think)
Navigation if you want a real offline satnav
iRuler
Word Lense
Trip Advisor
Booking.com etc
AroundMe
Tripit (although you can use the website with email watcher, i personnally simply get my trips automatically added to my iCloud calendar without doing anything)
Google Maps
Unity to convert any unit into another
AMP Bias and co
Polytune
Music Theory Tutorials
Guitar Pro
cubasis
Star Walk
best for photo for me is "Photo Editor by Aviary / Aviary" it's basically the Adobe editor, they offered all their filters and goodies for free recently, if it's still the case you'll be covered for ever for your on-the-go photo editing. Makes your girlfriend very happy when you can take a picture of her cat and make it look beautiful
Luminance is my #2
Paper
Flickr
Facebook Twitter Instagram and co
Tapatalk for here
Shazam
Whatsapp / Line / Kik
Spotify
Duolingo to learn languages
EasyFTP for iphone
Runkeeper / Runtastic
1Password is a must if you use it on your computer as well
CineXPlayer is my multimedia reader of choice, I keep a couple other when it can't open the odd file
+ have a look at your phone provider apps (I get my invoices in them), local taxi companies or global taxi app, the bus companies app can have an iphone payment app, etc etc