As others have pointed out, there's the strict mode now which is still quite restricted (pun intended), but what you most often don't hear is that you can also use check constraints, as in

    sqlite> create table t ( id integer primary key, n integer check ( typeof( n ) = 'integer' ) );
    sqlite> insert into t ( n ) values ( 1 );
    sqlite> insert into t ( n ) values ( '1' );
    sqlite> insert into t ( n ) values ( true );
    sqlite> insert into t ( n ) values ( 'x' );
    Runtime error: CHECK constraint failed: typeof( n ) = 'integer' (19)
    sqlite> select * from t;
    ┌────┬───┐
    │ id │ n │
    ├────┼───┤
    │ 1  │ 1 │
    │ 2  │ 1 │
    │ 3  │ 1 │
    └────┴───┘
    sqlite> select ( select n from t where id = 1 ) = ( select n from t where id = 2 );
    1 // i.e. true

Check constraints do have the advantage over more classical types that additional constraints can be declared such as valid ranges for numerical types etc.