Currently, owing to a bug, scp in Kubuntu and Ubuntu 9.10 (Karmic Koala) does not allow you to autocomplete remote directories (when you have a passwordless ssh setup, obviously).
While I have submitted a patch for review, this will not be backported into 9.10 and so, those who wish to have this functionality, should follow these steps:
Visit this bug to read about the problem. Note that this is a problem with bash-completion, not with scp itself.
Download my fix: bash-completion scp fix for Ubuntu 9.10.
Backup your current file:
sudo cp /etc/bash_completion.d/ssh ~/ssh_backup
Copy the downloaded file to /etc/bash_completion.d/:
sudo cp ./ssh /etc/bash_completion.d/
Restart your bash session and you should have working scp remote completion! ie. scp remotehost:~/myfi[TAB] will complete to remotehost:/home/you/myfile.txt
Note: I am not responsible for any damage this causes - it is not an official patch and I am unable to provide tech support. If you find problems with the fix, please report them to the official bug posted above which is more likely to get a response.
If anything goes wrong, you can restore the old configuration using:
sudo cp ~/ssh_backup /etc/bash_completion.d/ssh