I use jquery-chosen for my comboboxes.
If the combobox is at the bottom of the screen it can not be dropping down. Is there a way to get a list of drop up instead of down?
Link of demo-page: http://harvesthq.github.io/chosen/
So I make combobox without search:
$(".chosen-select").chosen({disable_search_threshold: 10});
                It's old, but i've searched for this feature and came across this article. Here is what i have added to Shawn Millers Answer for rounded corners, etc.
jsfiddle
.chosen-container .chosen-drop {
  border-bottom: 0;
  border-top: 1px solid #aaa;
  top: auto;
  bottom: 40px;
}
.chosen-container.chosen-with-drop .chosen-single {
  border-top-left-radius: 0px;
  border-top-right-radius: 0px;
  border-bottom-left-radius: 5px;
  border-bottom-right-radius: 5px;
  background-image: none;
}
.chosen-container.chosen-with-drop .chosen-drop {
  border-bottom-left-radius: 0px;
  border-bottom-right-radius: 0px;
  border-top-left-radius: 5px;
  border-top-right-radius: 5px;
  box-shadow: none;
  margin-bottom: -16px;
}
With Twitter Bootstrap the last margin-bottom would be something like -3px.
Thanks Gordon! Just to add to your response, here is another option.
CSS:
.chosen-container .chosen-drop.dropup {
  border-bottom: 0;
  border-top: 1px solid #aaa;
  top: auto;
  bottom: 40px;
}
.chosen-container.chosen-with-drop .chosen-single.dropup {
  background-image: none;
}
.chosen-container.chosen-with-drop .chosen-drop.dropup {
  box-shadow: none;
  margin-bottom: -16px;
}
JS:
$("select[dropup]").next().find(".chosen-drop").addClass("dropup");
$("select[dropup]").next().find(".chosen-single").addClass("dropup");
HTML:
<select id="selChosen" dropup style="width: 250px"></select>
                        Not a huge fan of the large amount of CSS the Chosen plugin comes with, but I was able to override some styles to make it happen. End result looks like this:
.chosen-container .chosen-drop {
    border-bottom: 0;
    border-top: 1px solid #aaa;
    top: auto;
    bottom: 40px;
}
                        I do that only for some components wrapping the selector with a span. In that way, I can control when the component goes down or goes up.
span.dropUp .chosen-container .chosen-drop {
    border-bottom: 0;
    border-top: 1px solid #aaa;
    top: auto;
    bottom: 40px;
}
span.dropUp .chosen-container.chosen-with-drop .chosen-single {
    border-top-left-radius: 0px;
    border-top-right-radius: 0px;
    border-bottom-left-radius: 5px;
    border-bottom-right-radius: 5px;
    background-image: none;
}
span.dropUp .chosen-container.chosen-with-drop .chosen-drop {
    border-bottom-left-radius: 0px;
    border-bottom-right-radius: 0px;
    border-top-left-radius: 5px;
    border-top-right-radius: 5px; 
    box-shadow: none;   
    margin-bottom: -16px;
}
And in the html put it in that way.
<span class="dropUp">
        SELECT                              
</span>
Only the select wrapping with the span component would drop-up the list
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