Getting started with PostGIS?
This question has been converted to Community Wiki and wiki locked because it is an example of a question that seeks a list of answers and appears to be popular enough to protect it from closure. It should be treated as a special case and should not be viewed as the type of question that is encouraged on this, or any Stack Exchange site, but if you wish to contribute more content to it then feel free to do so by editing this answer.
A good start can be the PostGIS Manual edited by Paul Ramsey. Boundless' Introduction to PostGIS
Boundless (formerly opengeo) has a very very good workshop with a lot of exercises on the PostGIS database. I would start with this one.
Some starting points to consider:
PostGIS in Action (Second Edition) should be your first resource
Materials from BostonGIS webpage
Also, for general introduction to PostgreSQL I quite enjoyed 'Beginning Databases with PostreSQL' book by Matthew & Stones.
My way to find PostGIS was http://bostongis.org/?content_name=postgis_tut01#20
there is three parts of the tutorial. I really like it.
Then I have to mention: http://postgisonline.org
I have tried to build a way of trying spatial SQL queries online. There are a very few tutorials there: http://postgisonline.org/tutorials
anyone can write a tutorial and use it through the site. Look at http://postgisonline.org/doc There is still a lot to do with the site but there is not time enough.
Take a look at Portable GIS:
provide beginners with a ready-installed and configured stack of open source GIS tools that would run in windows without the need for emulation or a live cdemulation or a live cd
i.e. You can have it up and running on a USB stick. Very handy for workplace environments.
It has on it:
PostgreSQL (version 8.4)/Postgis (version 1.4)