Now that CC has announced it’s Public Domain Mark, it’s worth going back through the difference between an assertion and a dedication.
First, just so everyone is on the same page. The public domain means that the work is out of copyright, either because copyright expired or because copyright didn’t cover the work in the first place.
A Public Domain Assertion is someone other than the the author of the work stating that they believe the work to be in the public domain. So if you found something some 18th century text or the works of Shakespeare (or perhaps a US Government work), you would use an assertion to let other people know that it was in the public domain. PD Assertions are a bit like tagging.
A Public Domain Dedication is what you use if you are the rightsholder of the work. The righstholder is often but not always the author of the work. PD dedication tools allow you to give up all of your rights over the work, and typically these tools cover copyright, database rights and contract. It’s a tool to take work in copyright now and place it into the public domain ahead of schedule from the typical life-of-the-author-plus-70-years formula.
In terms of tools to do both of the above, Creative Commons has both an assertion tool and a dedication tool (CC0), both of which cover a wide variety of content. Open Data Commons has a dedication tool — the PDDL — aimed at one specific type of material — databases.