What is a "database"? There was lot of discussion in this question: What database technologies do big search engines use?

So much discussion that it made me confused. So... what is a database, anyway? Are only relational databases "databases"? Are object-oriented databases "databases"? Is any system that allows me to store and retrieve information (like a map, list, etc) a database? 

Or does a database have to store/retrieve information and also have some administration features like Users and Privileges? Was dBase III plus a database, since it wasn't really relational?
I will quote Dictionary.com, as I take this as the meaning of database:


  a comprehensive collection of related data  organized for convenient access, generally in a computer. 


Under this definition, you can consider a database anything from a full-fledged RDBMS (SQL Server, Oracle, etc.) to a basic flat file.  If it stores data, it technically can be considered a database.

Now, like most things in our modern world, there's the accepted meaning of a name.  And in the case of database, that will vary from person to person.  A lot of people think of a database solely as an entity managed by a data system.

It is worth noting @FrustratedWithFormsDesigner's comment:


  card-catalogues would also count if you removed the "...generally in a computer".


I agree with that statement, and I don't necessarily think that a database needs to live in a "computer" or any electronic device.  A card-catalogue is a perfect example of a non-computerized database.