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From: Jamie Holly

Doing a join doesn't return the query interface, but rather the alias that was assigned to the joined table. Since variable assignment is processed left to right once it processes the ::join method your $users variable now contains the table alias.

What you want to do is stop your chaining before any methods that don't return the SelectQuery object you are building:

$query = db_select('user_badges_user', 'ubu')
        ->fields('u', array('uid', 'name'))
        ->condition('ubu.bid', $badge->bid); // Up to here you get a SelectQueryInterface returned and assigned to query
$query->join('users', 'u', 'u.uid = ubu.uid'); // Calls the join method on $query, but doesn't assign the return;
$users = $query->execute(); // Returns the DatabaseStatementInterface that you pull your results from

Generally I try to add joins at the beginning of the construction. It seems to make it easier to read (it seems most of Drupal's core code does the same), so I would write this query like this:

$query = db_select('user_badges_user', 'ubu');
$query->join('users', 'u', 'u.uid = ubu.uid');
$query->fields('u', array('uid', 'name'))
            ->condition('ubu.bid', $badge->bid);
$users = $query->execute();

You could assign $users when you add the fields and conditions, but this does make it easier if you want to add anything else to the query down the road.

Easiest thing to remember is that if you get a non-member/non-object error, then the item right above that doesn't return the proper class and you should stop variable assignment there and instead just call the method without assignment (ie: $query->join('users', 'u', 'u.uid = ubu.uid')).

Chaining might look a little better and save a few keystrokes,  but it really doesn't bring any performance enhancements and can keep headaches to a minimum, especially when working on classes you aren't that familiar with.