IG Index - Actually quicker and easier to use than the "proper" site.
Sky Sports Football Score Centre - Lets you choose "your" teams, plus instant access to all other scores, league tables, fixtures etc.
TV Guide - Quick and easy guide for virtually all channels at a glance as a list or in grid form, can scroll up and down channels individually with synopsis too. Very handy
Shazam - Useful if you hear a song on an advert of something and it bugs you for ages what it's called, this puts a stop to that
Google - I know it's easy enough to use the proper online Google site, but this is even quicker and easier, with voice controls too without having to "teach" it, and is quite accurate unless you have a daft accent
Twitter - Again, I find this simpler and easier to follow than proper online Twitter
Around Me - Quick and easy way of finding things wherever you are if you're not familiar with the area.
Currency Converter - Very useful and accurate for buying things online from any country
The Moron Test - Is a good laugh
Amazon - Very good app, takes the "fiddliness" out of using the proper Amazon site on your phone.
Met Office - The most comprehensive weather app by far
Torch - Very useful, can use either the screen or the camera flash, which is nice and bright
Grand Theft Auto: Chinatown Wars - Controls can be slightly awkward, but by far the best game on there
Trapster - Very good speed camera detector