Update (2017): The following two libraries have now become the most common drop-down libraries used with Javascript. While they are jQuery-native, they have been customized to work with everything from AngularJS 1.x to having custom CSS for Bootstrap. (Chosen JS, the original answer here, seems to have dropped to #3 in popularity.)
- Select2: https://select2.github.io/
- Selectize: http://selectize.github.io/selectize.js/
Obligatory screenshots below.
Original answer (2012): I think that the Chosen library might also be useful. Its available in jQuery, Prototype and MooTools versions.
Attached is a screenshot of how the multi-select functionality looks in Chosen.