MySQL is SQL software used most commonly with PHP as part of a LAMP stack. It competes very directly with DB2 which IBM supports on Linux/Apache. However, unlike DB2 it's free software under GPL.
The current release, 5.0, has almost all the features of the latest alpha, 5.2, which includes the Falcon engine which implements many features that DB2 and Postgres had in 1980, especially transaction features - summarized as ACID-compliant. However, no XA transaction support is included, not even for durable two phase commit yet.
Mediawiki and most thumbnail gallery software uses it to store all underlying data. Tikiwiki can also use it though it can stores its data in other less restrictive means.