On my iPhone I have a Gransnet icon which takes me straight here. Often. I'm not sure quite how I set it up, probably via Safari (which again I use often).
Otherwise the ones I use most are Google, Sky News (despite loathing the Murdochs), BBC News, Wikipedia (very, very useful), Met Office, Slimming World (not really up to the job, they say they're re-launching an improved version soon), the Maps app that came on the iPhone (again I use this all the time. It seems to be able to find any named place anywhere in the world) and BBC Radio 3 and Radio 4 icons, which are very useful for telling you exactly what's on the radio ie who's talking or the name of a piece of music, even what time a programme is due to end.
Maybe I'm being a bit iffy about the difference between an app and an icon.
I have lots of others on my phone eg recipes, radio stations of the world, quizzes, tourist guides, restaurant guides, games, social network apps etc which I never touch.
The other one I use a lot on my phone is the alarm clock/timer, esp when I'm cooking! Or sleeping. Very insomniac tonight though, look at the time of this post.