General

You can think of it as del.icio.us but designed to be embedded within any application.

Homepage: http://tasty.python-hosting.com/
Language: python
Interface: REST (Since the interface is just REST, it can be embedded in an application written in any programming language)
License: GPL
Database: PostgreSQL
Example: http://thraxil.org/ (browsing tags crashes .. http://thraxil.org/users/anders/tags/bile/)

tagging part

Described at: http://tagschema.com/blogs/tagschema/2005/06/slicing-and-dicing-data-20-part-2.html

Seems to have a speed-optimized and scalable database-structure:

“If you're interested in scalable architectures for folksonomy applications then let me just whet your appetite by saying that the two way association tables are used for answering questions about pairs of entities e.g. “What are all the Items for this User?” Or “what are all the Tags for this Item?” And this will scale to millions of Users better than any other schema.”