List all packages containing the words route or routing in their description:
aptitude search '~drout(e|ing)'
List installed packages that are not official Debian packages:
aptitude search '~S~i!~Odebian'
List packages installed from experimental:
aptitude search ~S~i~Aexperimental
List packages with 'ruby' and 'gtk' in their names:
aptitude search 'ruby gtk' aptitude search ~nruby~ngtk
List installed packages that depend on bash:
aptitude search ~S~i~Dbash
Purge all packages that have been removed except for their config files:
aptitude purge ~c