Off-Screen navigation button
#Huawei

Shake to change wallpaper
#Huawei

Screen that is curved along the vertical axis
#Samsung

Tilt actions

Check time/Skip songs/Swipe photos by tilting phone on its curve
#Samsung

Volume control by edge swipe
#Huawei

Motorola Flipout
#Motorola

Secondary display on hardware keyboard
#LG

Physical keyboard on back of the phone that can be opened
#Motorola

Custom screen-off gestures
#Bluboo

Draw to search emoji
#Google

Linux on Dex
This allowed you to run linux applications inside desktop mode.
#Samsung

Two fingerprint sensors
#Huawei

Xenon flash
It was available in Samsung S4 Zoom and K Zoom and it was in testing phase of Xperia Z1 prototype
#Samsung

Gesture to Rotate Screen
#Smartisan

Swipe to Clear Icon Badges
#Smartisan

Fullscreen album cover on lock screen
#Google

Samsung Pay MST
#Samsung