Perl 6 is an extensively refactored, super-modernized, and ultra-supercharged derivative of Perl 5. Simple things will still be simple to do, but you'll have enormously more "syntactic compound leverage" and "semantic overdrive" available for tackling challenging tasks.
Also see Juerd's Refuting Perl 6 Myths. (A slight correction to Juerd's slides: it is Perl 5.10 that will have many Perl 6 features you can start using. These will be in feature.pm, which is currently part of the Perl 5.9 developer branch.)
See the documentation section below for much more information.
The Long Perl 6 Super-Feature List
The Long Perl 6 Super-Feature List This list was moved to its own page so that there would be plenty of room for people at add additional explanations of what these features are, and to explain why they are Very Good Things (tm).
More Answers
Larry Wall (2006): Perhaps the Perl 6 slogan should be "All Your Paradigms Are Belong To Us". We'll get to that.
Damian Conway (2003): The Perl 6 design process is about keeping what works in Perl 5, fixing what doesn't, and adding what's missing. That means there will be a few fundamental changes to the language, a large number of extensions to existing features, and a handful of completely new ideas. These modifications, enhancements, and innovations will work together to make the future Perl even more insanely great — without, we hope, making it even more greatly insane.
Perl 6 is still under construction. So don't make critical plans that depend on it just yet. However, please see other sections below about intermediate Perl 6-related solutions you can use now (or soon, as in Perl 5.10, which will feature several Perl 6 features).
Crazy (in a good way).
Perl 5 : Swiss Army Chain Saw == Perl 6 : Swiss Army T-X Terminator (on the side of humans in this case).
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Perl 6 News
Planet Perl 6 blog aggregrator (The best general news source for Perl 6. It would be very helpful if others selectively copied the most useful information from this great resource into appropriate sections of this wiki.)
The O'Reilly Perl website sometimes has interesting articles about Perl 6. (Need to search for them.)
Some design influences on Perl 6
"Perl Best Practices" by Damian Conway. Even though this currently applies to Perl 5, most of the principles also apply to Perl 6. This book is a semi-officially recommended guideline for people doing develop core Perl 6 modules and tests.
Traits are one of the "Big Ideas" that have had some influence on #perl6 design discussions.
"The 100 Year Language" Useful information on how we should view Perl 6 (although it's not about Perl 6).
Perl 5 modules implementing Perl 6 features
In Perl 5.9 (development branch) and Perl 5.10 (production release), feature.pm provides some Perl 6 features that you will be able to selectively turn on.
There are many modules that currently implement parts of Perl 6 in Perl 5. Go to CPAN and do a module search on perl6.