Have you found the SQLLite extension to be one that is commonly built into PHP? It wouldn't do me any good to write it to use this extension if the guys that can't get a MySQL db also can't use the SQLLite module.
According to the PHP manual: in PHP 5, the SQLite extension and the engine itself are bundled and compiled by default. However, since PHP 5.1.0 you need to manually activate the extension in php.ini (because it is now bundled as shared). Moreover, since PHP 5.1.0 SQLite depends on PDO it must be enabled too.
I think that pretty much renders the SQLite extension useless for new scripts. The SQLite extension uses the SQLite 2.8.x format of database files (or file, rather, since each database is in exactly one file) while the SQLite driver from the PDO extension uses the SQLite 3.3.x (compatible with SQLite 3.4.0) format of database files.
It also means that you do not have a guarantee that SQLite will be available for your script users since the PDO extension might not be enabled, especially if the MySQL extension is not enabled.
If you don't think it's very common, do you know of any other alternative that might serve the purpose?
It is very commonly available (at least where PHP5 is available, and now that PHP4 is reaching end of life, PHP5 should be available), but so is the MySQL extension (and even more so, since it was popular in PHP4). As such, if MySQL is not available, there would be reason to suspect that SQLite may not available. On the other hand, it is possible that since no database server needs to be setup and configured, a host may still offer SQLite support even without MySQL support.