13.04 and later (GUI) (also works on Ubuntu Unity 22.10)

Follow-on-focus settings can be set using the unity-tweak-tool

12.10 and later (command line)

The following controls follow-on focus

gsettings set org.gnome.desktop.wm.preferences focus-mode 'sloppy'

or

gsettings set org.gnome.desktop.wm.preferences focus-mode 'mouse'

Use the value 'click' to reset to the standard focus-control.

Note: the difference between 'sloppy' and 'mouse' is described at the bottom of this answer.

In addition you have the following option which when set, automatically raises the window to have focus:

gsettings set org.gnome.desktop.wm.preferences auto-raise true

You can control the delay for this auto-raise capability (in milliseconds):

gsettings set org.gnome.desktop.wm.preferences auto-raise-delay 500

You can change raise-on-click to control what window is on top:

gsettings set org.gnome.desktop.wm.preferences raise-on-click false

12.04

Two methods for 12.04 are presented below:

method 1

Use gconf-editor and change the focus-mode value shown to mouse or sloppy

(see note below)

If do not have gconf-editor already installed then you can install via the terminal command:

sudo apt-get install gconf-editor

In addition you have the following key which when set, automatically raises the window to have focus - auto-raise.

You can control the delay for this auto-raise capability (in milliseconds) by changing the key value auto-raise-delay

method 2

use gnome-tweak-tool

change windows focus mode to mouse or sloppy

(see note below)

"mouse" vs "sloppy"

A focus mode "sloppy" seems to work better at allowing Alt+TAB to override focus.

"mouse" means that if the mouse isn't in the window, the window isn't selected, no matter what you've selected in any other way.

The window focus mode indicates how windows are activated. It has
three possible values; "click" means windows must be clicked in order
to focus them, "sloppy" means windows are focused when the mouse
enters the window, and "mouse" means windows are focused when the
mouse enters the window and unfocused when the mouse leaves the
window.

Controlling What Window is on Top

The following window options control what window is in the front of others (or "on top"). It's slightly different than what window has the input focus. The following descriptions help explain slightly.

raise-on-click

Some users who use focus-follows-mouse do not like the windows the interact with to come to the top unless they explicity click on the tilebar of the window. This gives a finer grain of control when working with multiple windows, but can be frustrating for most users.

auto-raise

Some users who use focus-follows-mouse, like to have the window their cursor is over automatically raise to the top. This makes the window in full view, with no other windows eclipsing it.

auto-raise-delay

The length of time to wait before triggering the auto-raise behavior.