We can mention the apps which we are using on our iOS devices with a short description but please do not mention the usual like ICICI or any banking app or facebook and such.
My list..
AV Player / nPlayer : For playing videos of almost any format. I used AV Player a lot before but then started to use nPlayer because it as faster seeking of video and gesture controls better than AV Player (IMO).
iTV Shows 2: This is the ONLY app I use to keep track of TV shows that i watch and download (separate copies of same app i have, one for tracking watched and other for downloading). I would strongly recommend this app for people wanting to track TV shows on their iOS device. And believe me i have a folder with around 11 tv show apps and i use none of them).
m-Indicator: Only for Mumbai people, fare of auto and taxi and local train timetable and lots more. Previously it was only for android but not there is iOS app as well. Another app is iLocalMumbai
CityMaps2Go: Awesome app for offline maps (no navigation) and offline search as well. Have used it internationally only so no idea about usefulness in India.
Toshl Finance: Recently discovered and only app i liked for tracking my finances. The main reason for liking is because i can put tags (not categories) for my expenses. I do not like the apps that have categories like Food, Coffee, Conveyance. Grocery etc. Instead here i can put things like Carrot, Auto Rickshaw, Pizza Hut, Shiv sagar and whatever i want, it is user made tags and once you make a new tag, it is stored and can be reused. Simply awesome app.