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