This process will work for Ubuntu 11.04 (Natty) and older versions. For the newest versions please refer to this Answer by RolandiXor. Thank you.

Not tested by me, but found in a link provided at: http://ubuntuforums.org/showthread.php?t=393425, I hope this may help.

Install joystick and jscalbrator

sudo apt install joystick jscalibrator

then run the calibration processes

jscal -c /dev/input/js0 (this is my joystick location, check yours)

jstest /dev/input/js0 (or wherever) If I remember correctly, this should return 0 for no error.

run jscalibrator

jscalibrator

and it should recognize the type of gamepad correctly and recognize all of your buttons, and axis

There is also an application called jstest-gtk, which seems to do something like that, I post here a screenshot and the link for you: https://github.com/Grumbel/jstest-gtk (This software may need to be compiled in order to make it work)

It is possible to calibrate Joysticks in Kubuntu using KDE's system settings. This is a bit of an "overkill" solution, as of course it requires KDE (and most Ubuntu users will not want this).

I did not have my joystick plugged in for the above screenshot, but I have tried it before and it works.

JStest gtk and joystick

These are two tools included in the Ubuntu repositories that I have not tested recently (I found these when looking for other options). The first of the two, jstest-gtk, is a graphical tool, and joystick is a set of commandline utilities.

You can install them using:

sudo apt-get install jstest-gtk 

or

sudo apt-get install joystick

Jstest-gtk is a front end to joystick's commandline tools.

I'm using Ubuntu 13.04 and have Logitech Rumblepad 2. And what I did was installing these, joystick and jstest-gtk. It's already been calibrate to default and joystick device is detected right. Just plug and play.

If you need to calibrate and save your configuration you can do this, open jtest-gtk, You will see this,

You can calibrate by double click on the device.

Hope it will help you out as it has done to me.

Thanks to @B. du Garay for pointing out in comments that anti-micro is now available in the repository (20.04 only), install it with:

sudo apt install antimicro

The answers here are getting a bit old now, and users seem to be having issues again, so this is a 2016 solution to configuring your joystick or gamepad on Ubuntu.

You can use antimicro, it is a fork of joy2key and has a GUI, use this PPA for 12.04 to 15.10

sudo add-apt-repository ppa:ryochan7/antimicro
sudo apt-get update
sudo apt-get install antimicro

For 16.04+ use this PPA

sudo add-apt-repository ppa:nilarimogard/webupd8
sudo apt-get update
sudo apt-get install antimicro

Source

I am currently using qjoypad for mapping keys (even the mouse) to a Logitech Gamepad F310. It's working well for games that are designed with only keyboard and mouse controls in mind. It seems to require being run from cli as qjoypad --notray. It does use a GUI.

How to Install Qjoypad
First add the GetDeb Games ppa

wget -q -O - http://archive.getdeb.net/getdeb-archive.key | sudo apt-key add -
sudo sh -c 'echo "deb http://archive.getdeb.net/ubuntu raring-getdeb games" >> /etc/apt/sources.list.d/getdeb.list'

Then update and install package

sudo apt-get update
sudo apt-get install qjoypad

Alternatively download the package here and install with your favorite package manager.