$('.ui-input-clear').live('click', function(e){
alert('click!');
});
Good starting point. I use livebecause the search is not necessarily located on the page when loading. This, of course, is not specific using the class, but you can do so if necessary.
Update: In jQuery 1.7 .livedeprecated in favor .on: http://api.jquery.com/on/
$('.ui-content').on('click', '.ui-input-clear', function(e){
alert('click!');
});