It's trivially easy to copy a SQLite database. It's less trivial to do this in a way that won't corrupt it. Here's how:

  shell$ sqlite3 some.db
sqlite> begin immediate;
<press CTRL+Z>
shell$ cp some.db some.db.backup
shell$ exit
sqlite> rollback;

This will give you a nice clean backup that's sure to be in a proper state, since writing to the database half-way through your copying process is impossible.

Thanks to Habbie for this info!