Off the top of my head, from recent usage:
Nova Launcher
RealCalc Plus
Business Calendar 2 (though I have multiple calendar apps installed, no one is best for everything)
Squid (formerly Papyrus) (on my tablet, for annotating documents)
Ghostery (currently my most-used browser)
Maps.ME (need to test the supposedly improved offline features of Maps though)
Chomp SMS
AquaMail/MailDroid Pro (AquaMail makes better use of the tablet's screen, on a phone I could use either, both have minor features I prefer)
Train Times UK (live departure board widget on one of my homescreens)
PowerAmp or Neutron (yes, I have and use both, e.g. a long, on-going series or audiobook on one while switching to the other for music).
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your 10 favorite applications , you can't live without
