Is it possible to access an SQLite database from JavaScript?
Actually the answer is yes. Here is an example how you can do this: http://html5doctor.com/introducing-web-sql-databases/
The bad thing is that it's with very limited support by the browsers.
More information here HTML5 IndexedDB, Web SQL Database and browser wars
PS: As @Christoph said Web SQL is no longer in active maintenance and the Web Applications Working Group does not intend to maintain it further so look here https://developer.mozilla.org/en-US/docs/IndexedDB.
SQL.js
EDIT
As @clentfort said, you can access SQLite database with client-side JavaScript by using SQL.js.
You could use SQL.js which is the SQLlite lib compiled to JavaScript and store the database in the local storage introduced in HTML5.
Up to date answer
My fork of sql.js has now be merged into the original version, on kriken's repo.
The good documentation is also available on the original repo.
Original answer (outdated)
You should use the newer version of sql.js. It is a port of sqlite 3.8, has a good documentation and is actively maintained (by me). It supports prepared statements, and BLOB data type.