Where are some useful SQL puzzles to teach SQL in a workplace? I'm looking for beginner and intermediate level SQL puzzles, that I can point trainees at for practice.

I'm aware of http://sqlzoo.net/ which is a great resource - is there anything else out there that you could suggest?
Joe Celko's books and newsgroup posts are a good source of puzzles (with a variety of answers). They might be a bit more intermediate/advanced and not MySQL-specific, but are easy to follow and generally come from practical real-world situations.

Particularly, hunt down a copy of Joe Celko's SQL Puzzles and Answers (link to Google preview), it's a compilation of some of the best.

The SQLTeam forums occasionally have some interesting problems too, but generally focused on MS SQL Server.

The HackerRank SQL domain has a variety of SQL challenges that can be completed using multiple implementations (e.g.: Oracle, MySql, MS SQL Server, DB2).