Some desktop environments don't provide a way to change the mouse acceleration (GNOME and Unity for instance), and even for those that do (like Cinnamon), you can't completely turn it off. Here's how to completely disable mouse acceleration in Linux (for Xorg).
Disabling mouse acceleration is useful for FPS gaming. Mouse acceleration makes the pointer movement depend on the speed with which you move the mouse, accelerating as you move it faster. So moving the mouse across the same distance can have different results, based on movement speed. In FPS games, this can make aiming difficult.
With mouse acceleration disabled, the movement of the pointer is the same as the movement of the mouse, and it doesn't change based on the movement speed. As a result, your aim should be more accurate in first-person shooters.
To completely disable mouse acceleration, create a file called "50-mouse-acceleration.conf" in xorg.conf.d. The path to xorg.conf.d can vary depending on the Linux distribution you use. For instance, in Ubuntu, Linux Mint, and derivatives, it's /usr/share/X11/xorg.conf.d/. On Arch Linux, it's /etc/X11/xorg.conf.d/.
To open an empty 50-mouse-acceleration.conf file in /usr/share/X11/xorg.conf.d/ with Nano (command line text editor; should be installed by default in most Linux distributions), use the following command:
sudo nano /usr/share/X11/xorg.conf.d/50-mouse-acceleration.conf
And in this file, paste the following:
Section "InputClass" Identifier "My Mouse" MatchIsPointer "yes" Option "AccelerationProfile" "-1" Option "AccelerationScheme" "none" Option "AccelSpeed" "-1" EndSection
Then save the file (to save the file in Nano, use Ctrl + o, then press Enter; to exit, use Ctrl + x). Note that the section just needs an identifier, but the actual name doesn't matter, so you don't have to replace "My Mouse" with anything.
Once you're done, restart the session (logout/login). That's it!
Using this, the Touchpad acceleration is left unchanged.