SQLite is indeed built into iOS and Mac OS X as well. Core Data's store uses SQLite as an option (XML and Binary are the others), and it is accessible via third party frameworks like FMDB.
Unfortunately, it's quite slow on Android. And make sure never to put your db on the sdcard, or else your whole phone becomes unusable while doing writes to the db.
SQLite is overall slow if you are writing item-by-item. Does not matter what platform you use. Write multiple items in single transaction. As well understand what you get and what you loose by writing all items in single transaction.
And iPhones, and BlackBerries. It is by far the most widely use relational DB in the world (despite what the MySQL people claim on their website, they're not even close)
