Since I'm an android user, I could recommend the following apps which are available at Google Play Store:
Student's Task Manager+ is a planner specifically designed for students. It's very lightweight and doesn't take up much space in the phone. Pretty handy to have.
A-Biology Level is rated highly in Google Play which helps students with biology. It contains detailed diagrams and explanations about certain topics.
Chemistry Mobile Free is a great app for chemistry students. Our has a periodic table, list of formulas, and more.
Mindjet Maps for Android is probably the best way to jot down ideas. Perfect for brainstorming.
Dropbox is one of the best cloud storage service providers. Students would definitely find this useful especially when transferring abs sharing various files.
Evernote is a very popular note taking application. Students should definitely have this on their mobile devices.
Students no longer have to worry about physics formulas if they have pocket physics installed in their mobile devices.
Maths Formulas gives all of the important formulas that students hate. This is a great reference tool when it comes to formulas.
This is one of the most useful apps that every student should have. The Merriam Webster dictionary is free to download and use.
Every mobile device has a pre installed calculator. But let's face it, they're crap. RealCalc Scientific Calculator adds a lot more functionality to the default calculator of mobile devices.
So, that's my list.