The first type of licences are public-domain-like licences, also known as BSD-style licences, Permissive free software licences, or “Copycenter licences”. These licences allow you to do almost anything conceivable with the program and its source code, including distributing then, selling them, using the resultant software for any purpose, incorporating into other software, or even converting copies to different licences, including that of non-free (so-called “proprietary”) software.
Probably the only two actions none of these licences allow is removing the original copyright notice, or suing the creator of the software for damages (the latter is due to the “no warranty” clause). Some of them pose some additional that do not reduce from their public domain nature.
Prominent examples of Public Domain licences include:
The various BSD licences, under which the “Berkeley Software Development” UNIX variant were made available. The original 4-clause BSD licence contained an additional advertising clause, that required publishing the names of the copyright holders on every advertising material. This proved to be a problem and was rendered GPL-incompatible and so using this licence is no longer recommended.
Later on, the advertising clause was removed to formulate 3-clause and 2-clause BSD licences, which are both less problematic and GPL-compatible.
The MIT X11 Licence was created by MIT for their X Window System software. It explicitly allows to do many activities with the licensed code, including sub-licensing, which means converting derived works of the code to different licences.
the Apache Licence was formulated for the Apache project and has seen several revisions. It includes some language to deal with patent-related issues. The latest version - Apache 2.0 was partially created in order to be compatible with version 2 of the GPL, but the FSF ruled the Apache Licence as incompatible with it. The Apache Licence, however, was declared as compatible with version 3 of the GPL.
The ISC licence is functionally equivalent to the 2-clause BSD-licence, with some “language made unnecessary by the Berne convention removed”. This licence is also favoured by the OpenBSD project.