Post variables in mysql_query failing

[Mavent]

This works:
$result = mysql_query("SELECT * FROM mydatabase WHERE username = 'billybob'");

This does not:
$user = "billybob"
$result = mysql_query("SELECT * FROM mydatabase WHERE username = $user");

The second results in this error:
Warning: mysql_num_rows(): supplied argument is not a valid MySQL result resource

Doh. Forgot I was passing a string. Fixed it myself.