So when you create the options in the first place (using PHP or whatever?) you can just add a title attribute to each option.
If you want to add a title attribute using Javascript after the select box has been created, you can use the getElementsByTagName('option') collection of the select box like that
Code:
// get the select box named "myselect"
var mySelect = document.getElementsByName('myselect')[0];
// get all its options
var theOptions = mySelect.getElementsByTagName('option');
for(i=0; i<theOptions.length; i++) {
theOptions[i].title = 'This is title #' + i;
}