I am looking for a publicly available SQL database with free access, where one can run some SELECT
queries for free on some meaningful data (not item1, item2, item3
If SQL Server is an option then Northwind/Adventureworks are the standard "training" DBs. Do a search.
For mySql this project looks promising:
http://sourceforge.net/projects/awmysql/
Also, this might be a dupe:
Is there a "Northwind" type database available for MySQL?
Where can I download Northwind database for Postgresql?