Bootstrap 5+ (Update June 2022)
dropdown-menu-right has been replaced with dropdown-menu-end
<div class="dropdown-menu dropdown-menu-end">
STUFF
</div>
https://getbootstrap.com/docs/5.2/components/dropdowns/#menu-alignment
Bootstrap 3.1+
Adding the class .dropdown-menu-right to the same div containing the class dropdown-menu:
<div class="dropdown-menu dropdown-menu-right">
STUFF
</div>
http://getbootstrap.com/components/#dropdowns-alignment
Bootstrap 2.3 & 3.0
Add the class .pull-right to the same div containing the class dropdown-menu
<div class="dropdown-menu pull-right">
STUFF
</div>
This seems to work for me using bootstrap 3.0