BBC Weather – It’s functional, accurate and well designed.
Dashclock and the battery extension – A great widget that puts a lot of information in front of your face as quickly as possible.
Dots – Good game that actually takes a little brain power to get good at.
Snapseed – If you want some more photo editing options over the stock camera.
Google Keep is basically perfect for notes/reminders unless you’re planning on making hundreds.
Nerdy Stuff
Light Flow Lite – Allows you to set custom patterns and colours for the notification LED so you can tell whether it’s worth turning the screen on or not (e.g. I have it flash green rapidly for SMS and missed calls, but slowly and in yellow if it’s just an email.)
TASKER – My favourite app. A little bit of work makes your phone a lot smarter. For example, automatically turning sound and wifi on when I get home, silent mode at college. Also, it can be used to change the UI; I’ve got it leaving a permanent link to voice actions in the notification bar. 7-day trial if you go to their website.