Sky News is a good one. 0800 wizard to give alternative numbers, and 0870 another similar one. Shazam to identify music being played, this one is marvelous. Weather ones such as Met Office and Living Earth. Love Living Earth as it shows you the world in real time with cloud coverage and when it is dark or light.Angry Birds, Spider, Mahjong and Sudoku2. Tunein Radio is great.
Most of the above are free or just 69p. Many of the apps have free versions but you do have to put up with adds. This does not worry me, would rather have free ones.
The best thing is to go to the itunes store and then to apps and spend some time going through them. I always check out the reviews too.