For me Tapatalk (Paid App) (Or the HD version) (Reading forums in a clean clear manner). Is the main indispensable app
And Super Hexagon (Paid Game) one of the best games released in a long time.
Skifta (Free) is a really good DNLA app it works really well with well designed 3rd party hardware.
BubbleUPNP (Paid or limited / adware) is probably better if your hardware is picky / flaky.
Wifi File Explorer (Paid) is pretty good. Allows you to start a webserver on your device in one click then connect to it with a browser to pull the odd file. (It can zip up multiple files but it is not 100% reliable with files that are large numbers of GB).
ezpdf / Repligo - PDF Viewers I dunno which I think is the best. (The official Adobe Acrobat App is not very good except in rare cases where it is great (Normally when ezpdf / Repligo doesn't work properly - probably a specific publishing mode in Acrobat or InDesign or something not sure).
Mobialia Chess (Free or Paid) Best Chess Application. Can connect to FICS Free Internet Chess Server. Timeseal works so time is fair and people (Shouldn't ?) be able to cheat.
Adaway. Indispensable hosts file downloader to block ad's Google removed it from the play store so you need to get it from FDroid or its website. (It works pretty damn well I suppose that is why it was removed) you need to be routed to use it and it is 100% free.
Flashlight Widget - This one it works on all my devices and isn't adware : https://play.google....bgne.flashlight