Nothing too fancy, but these are my favorites (I'm excluding Google's stuff, which I probably use the most, but I feel like everyone is already familiar enough with these). Some of these require root.
Adguard - This is an adblocker that still works. Adfree Android stopped working at Nougat.
AllCast - Cast any file that's on your device to your Chromecast. Like, if you download a TV show or something, you can cast it.
Amazon Kindle - I haven't used a hardware Kindle since the Kindle 2, since this works so well.
Arkanoid vs Space Invaders - I just wanted to recommend this game.
Authy - It works like Google Authenticator but is better because you can cloud backup your codes and access them from multiple devices.
Barcode Scanner - Unobtrusive, simple.
Buycott - You sign up for the causes you want to support and then you can scan barcodes on items, and it'll tell you if you should avoid buying them. It helps for avoiding Koch and Nestle products, since they are very hard to completely avoid.
FlashFire (needs root) - You need this if you're rooted and want to install OTA updates. That's basically what it does.
handyCalc - Hands down the best calculator app I've used.
Laser Level - Simple level tool.
LastPass - Set complex passwords that you don't need to memorize.
Netflix - Works well.
Nova Launcher - This is the best launcher. I like that you can export and import you settings to new devices.
OneNote - I use OneNote on my Surface Pro, so this syncs it
Official TWRP App (needs unlocked bootloader) - This lets you easily update TWRP without having to manually flash it.
Plex - Stream videos from your library.
Pocket Casts - This is my favorite podcast app. Others are probably decent, but I like the flexibility and cloud sync capabilities.
QuickPic - I like this better than Photos; it's faster, and the UX feels more intuitive.
Root Explorer - This is a good file explorer.
Signal - Encrypted SMS.
Titanium Backup Pro (needs root) - This isn't quite as necessary these days, but it's nice to backup and restore your apps and app data (including sideloaded apps that Google won't transfer) between devices and/or wipes. Like, when I did the transfer from my Nexus 6P to my Pixel XL, a ton of apps failed to transfer. Titanium Backup easily restored them, as well as their settings.
Wifi Analyzer - I use this once in a while to see what Wifi access points are around, and which ones have the best signal.