MySQL is the database software that is the back-end storage for All The Tropes. If you see messages about MySQL, you're probably seeing error messages that the database has crashed, though some pages do reference MySQL even when the database is just fine. The admins will have it fixed shortly. Nothing to worry about too much.
("SQL", by the way, stands for Structured Query Language, and is a standard language for managing relational database systems. MySQL is one of numerous software systems that use it.)
Totally unrelated to My So-Called Life.
- Screwed by the Network: Monty Widenius' interest was sold to Sun Microsystems, which was fine for a while. Then Sun was sold to Oracle, another database company. Having no interest in maintaining a free product that competes with their major product, development has slowed, leading to...
- Start My Own: a few, notably MariaDB which was by Widenius himself. See the list of MySQL clones on Wikipedia.