Understanding GPL licenses

If your main motivation when writing software is to earn money on every installation, then make sure that those licenses are not made for you. But if you prefer helping the community, grow your project and receive help, code patches and bug reports from worlwide developers and users, just keep reading.
GPL are good licenses for your Open Source software but from the beginning since now they have been growing in number. That's the reason why there are various types of GNU/GPL Licenses, the most popular are: GPL, LGPL, and AGPL. There are also various versions: initial (also known as v1), v2 and the last one v3.
We are going to start from the beginning:

The GNU General Public License (GNU GPL or simply GPL) version 1 was originally written by Richard Stallman on February 1989 for his GNU project and is the most widely used free software license.

The license preamble is very explicit explaining the intention of the license: guarantee your freedom to share and change free software, and later explains that free refers to freedom and it's not relative to price.

Here we summarize the terms and conditions for copying, distribution and modification which are:

0 - To which programs apply this License Agreement
1 - You can copy and distribute copies of source code
2 - You can modify the your copy of the program or any portion of it
3 - You can copy and distribute the program in object code or executable if you accompany it with the complete source code
4 - You may not copy, modify, sublicense, distribute or transfer the program using any other non-GPL license
5 - By copying, distributing or modifying the Program (or any work based on the program) you indicate your acceptance of this license to do so
6 - You may not impose any further restrictions each time you redistribute the program
7 - The Free Software Foundation may publish revised and/or new versions of the General Public License
8 - If you wish to incorporate parts of the program into other free programs whose distribution conditions are different, write to the author to ask for permission
9 - BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
10 - IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES

Here comes the main difference between the GPL and LGPL (Library GNU Public License in his first version):

When code licensed under the GPL is combined or linked with any other code, that code must also then be licensed under the GPL. In effect, this license demands that any code combined with GPL'd code falls under the GPL itself.
Code licensed under the LGPL can be dynamically or statically linked to any other code, regardless of its license, as long as users are allowed to run debuggers on the combined program. In effect, this license recognizes kind of a boundary between the LGPL'd code and the code that is linked to it.

GNU Affero GPL, also known as AGPL:

AGPL license was designed for application services providers who didn't want to apply ordinary GPL license, AGPL does not force source code distribution when licensed software is being used to provide a service, tipically web applications.

Version 2

GPLv2:

GPL version 2 was published on June 1991. According to Richard Stallman, the major change in GPLv2 was the "Liberty or Death" clause in section 7. This section says that if somebody has restrictions imposed that prevent him or her from distributing GPL-covered software in a way that respects other users' freedom (for example, if a legal ruling states that he or she can only distribute the software in binary form), he or she cannot distribute it at all.

LGPLv2:

In 1999 version 2.1 of the LGPL was released, it was renamed to the GNU Lesser General Public License to reflect its place in the philosophy. The main purpose of this license for C libraries was to allow to replace the propietary ones. This license was less restrictive.

AGPLv2: There is no AGPL version 2

Version 3

Version 3 was released on May 31, 2007. This version introduces major changes to version 2, and the most important could be the ones related to software patents.

GPLv3:

According to Stallman, the most important changes are in relation to software patents, free software license compatibility, the definition of "source code", and hardware restrictions on software modification. Other changes relate to internationalization, how license violations are handled, and how additional permissions can be granted by the copyright holder.

Other notable changes include allowing authors to add certain additional conditions or requirements to their contributions.

LGPLv3:

LGPLv3 is more flexible and protective. The main difference, according to Simon Phipps, an OpenOffice developer: "Upgrading to the LGPLv3 brings important new protections to the OpenOffice.org community, most notably through the new language concerning software patent"

AGPLv3:

GPLv3 and AGPLv3 include section 13 to achive mutual compatibility of both licenses. This sections allow explicitly the convivence of both license and the program who emerges as combination of both keeps the restrictions of use and distribution over networks specified in AGPLv3.


References:

Wikipedia

OpenOffice.org licensing FAQ

SunMink

You can find a spanish translation on my website: "Entendiendo las licencias GPL".