This article is for 16.04, if you are looking for 16.10, it's here.

This article provides a list of many popular applications PPAs for Ubuntu 16.04 LTS Xenial Xerus. It provides PPA addresses for LibreOffice, GIMP, Inkscape, Scribus, SimpleScreenRecorder, OpenJDK, even GNU Ring, and some more applications (I listed only free software here, please tell me if I made any mistake).
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Important note:  every PPA is Personal meaning it could be created by any person. You may trust or distrust any of them, use one or not to use one. Use these PPA repositories on your own risk. 

LibreOffice
https://launchpad.net/~libreoffice/+archive/ubuntu/ppa

sudo add-apt-repository ppa:libreoffice/ppa
sudo apt-get update
sudo apt-get install libreoffice 

SimpleScreenRecorder

sudo add-apt-repository ppa:maarten-baert/simplescreenrecorder
sudo apt-get update
sudo apt-get install simplescreenrecorder 


HandBrake

sudo add-apt-repository ppa:ricotz/experimental
sudo apt-get update
sudo apt-get install handbrake 


GIMP
https://launchpad.net/~otto-kesselgulasch/+archive/ubuntu/gimp

sudo add-apt-repository ppa:otto-kesselgulasch/gimp
sudo apt-get update
sudo apt-get install gimp 

Inkscape 
https://launchpad.net/~inkscape.dev/+archive/ubuntu/stable

sudo add-apt-repository ppa:inkscape.dev/stable
sudo apt-get update
sudo apt-get install inkscape 


Blender
https://launchpad.net/~thomas-schiex/+archive/ubuntu/blender

sudo add-apt-repository ppa:thomas-schiex/blender
sudo apt-get update
sudo apt-get install blender 

GRUB Customizer 
https://launchpad.net/~danielrichter2007/+archive/ubuntu/grub-customizer

sudo add-apt-repository ppa:danielrichter2007/grub-customizer
sudo apt-get update
sudo apt-get install grub-customizer 

Boot Repair
https://launchpad.net/~yannubuntu/+archive/ubuntu/boot-repair

sudo add-apt-repository ppa:yannubuntu/boot-repair
sudo apt-get update
sudo apt-get install boot-repair 

Tor Browser

sudo add-apt-repository ppa:webupd8team/tor-browser
sudo apt-get update
sudo apt-get install tor-browser

VLC

sudo add-apt-repository ppa:videolan/stable-daily
sudo apt-get update
sudo apt-get install vlc 

Scribus 
https://launchpad.net/~scribus/+archive/ubuntu/ppa

sudo add-apt-repository ppa:scribus/ppa
sudo apt-get update
sudo apt-get install scribus 

Unetbootin 

sudo add-apt-repository ppa:gezakovacs/ppa
sudo apt-get update
sudo apt-get install unetbootin 

Terminix
https://launchpad.net/~webupd8team/+archive/ubuntu/terminix

sudo add-apt-repository ppa:webupd8team/terminix
sudo apt-get update
sudo apt-get install terminix 

Ubuntu SDK
https://launchpad.net/~ubuntu-sdk-team/+archive/ubuntu/ppa

sudo add-apt-repository ppa:ubuntu-sdk-team/ppa
sudo apt-get update
sudo apt-get install ubuntu-sdk-ide

Unity Desktop Environment
https://launchpad.net/~ubuntu-desktop/+archive/ubuntu/ppa

sudo add-apt-repository ppa:ubuntu-desktop/ppa
sudo apt-get update
sudo apt-get install unity 

Atom
https://launchpad.net/~webupd8team/+archive/ubuntu/atom/+index

sudo add-apt-repository ppa:webupd8team/atom
sudo apt-get update
sudo apt-get install atom 

GNOME Shell Extensions
https://launchpad.net/~gnome-shell-extensions/+archive/ubuntu/ppa

sudo add-apt-repository ppa:gnome-shell-extensions/ppa
sudo apt-get update

Eclipse
https://launchpad.net/~mmk2410/+archive/ubuntu/eclipse-ide-java

sudo add-apt-repository ppa:mmk2410/eclipse-ide-java
sudo apt-get update
sudo apt-get install eclipse-ide-java 


Android Studio
https://launchpad.net/~paolorotolo/+archive/ubuntu/android-studio

sudo add-apt-repository ppa:paolorotolo/android-studio
sudo apt-get update
sudo apt-get install android-studio 

Chromium
https://launchpad.net/~saiarcot895/+archive/ubuntu/chromium-dev

sudo add-apt-repository ppa:saiarcot895/chromium-dev
sudo apt-get update
sudo apt-get install chromium-browser 

FreeCAD
https://launchpad.net/~freecad-maintainers/+archive/ubuntu/freecad-daily

sudo add-apt-repository ppa:freecad-maintainers/freecad-daily
sudo apt-get update
sudo apt-get install freecad-daily 
 

Y PPA Manager
https://launchpad.net/~webupd8team/+archive/ubuntu/y-ppa-manager

sudo add-apt-repository ppa:webupd8team/y-ppa-manager
sudo apt-get update
sudo apt-get install y-ppa-manager 
 

Qt Creator
Note: this is Qt Creator binary packages created from Git source code. Thus its name is qtcreator-git. This PPA is maintained by Alexander Drozdov.

sudo add-apt-repository ppa:adrozdoff/qtcreator-git
sudo add-apt-repository ppa:beineri/opt-qt561-xenial
sudo add-apt-repository ppa:adrozdoff/llvm-xenial
sudo add-apt-repository ppa:adrozdoff/cmake
sudo apt-get update
sudo apt-get install qtcreator-git


LightTable

sudo add-apt-repository ppa:dr-akulavich/lighttable
sudo apt-get update
sudo apt-get install lighttable-installer 


OpenJDK 7

sudo add-apt-repository ppa:openjdk-r/ppa
sudo apt-get update
sudo apt-get install openjdk-7 


OpenJDK 8

sudo add-apt-repository ppa:openjdk-r/ppa
sudo apt-get update
sudo apt-get install openjdk-8 


KDE Connect

sudo add-apt-repository ppa:vikoadi/ppa
sudo apt-get update
sudo apt-get install kdeconnect 


GNU Ring

sudo sh -c "echo 'deb https://dl.ring.cx/ring-nightly/ubuntu_16.04/ ring main' > /etc/apt/sources.list.d/ring-nightly-man.list"
sudo apt-key adv --keyserver pgp.mit.edu --recv-keys A295D773307D25A33AE72F2F64CD5FA175348F84
sudo add-apt-repository universe
sudo apt-get update && sudo apt-get install ring


The latest PPA for 16.04 mentioned here is GNU Ring and added at 30 November 2016.


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