I'm planning on leaving the Android ecoscape once my current phone breaks down, or a tempting offer comes along. But until then I'm mostly content with the functionality itself. Recently flushed my Note 2 entirely and slapped on the last nightly cyanogenmod, a process that was surprisingly smooth despite Samsung's bootloader and Knox.
Once everything was back up and running I trimmed the fat, a lot of the apps I had previously kept installed simply weren't interesting enough to re-download. Here's a list of the ones that were, and thus are the apps I can't live without.
K9 - E-mail client deluxe.
Baconreader - Reddit, oh thou art a beast.
Firefox - Them plugins.
Inoreader - I was using selfoss for months, but this is smoother.
Orbot - Tor, can't live without you.
Simpletasks cloudless - todo.txt, perfectly executed.
Analytics - For now, at least.
Whitepapers link - Scanning of specially marked papers.
Bankdroid - Not sure about internationally, but fantastic bank widget.
ezPDF - Pretty much reads everything I throw at it. Always has.
Keepass2android - Works perfectly with KeePassX.
Officesuite pro - Handy at (rare) times.
Foldersync - Works fantastically with encfs shares.
Beyondpod - Podcast perfection.
Chromecast - For, well, our chromecast.
Netflix - For now, there's finally cropping up alternatives.
Quickpic - Everything an image viewer should be, and nothing else.
Spotify - What are these MP3s you speak of?
VLC - Really not the best, just a personal favourite.
Sleep as android - Best alarm clock I've ever found.
Solid explorer - Unsurpassed file manager and network share access.
Tasker - Automation, automation, automation.
Appsales - For the cheapskate within.
Skånetrafiken - Swedish public transport system.
Twilight - Dims and reddens your screen, to preserve your eyes.
Fing - Network mapper. Glorified ping tool, but it works great.
Muzei - Wallpaper downloader for classical art.
Minimalistic text - Use it mostly for tasker variables.
Widget locker - Because other lock screens are terrible.
This will likely be my final list. I did install some additional apps, but they aren't what I'd call essential. Hopefully you'll find some new favourites in this list.