Kmail

Transfer mail and settings to another computer (or another user account on the same machine)

Solution: The messages are typically in ~/.kde/share/apps/kmail/.

For very old installations of KMail, the messages can also be in ~/Mail.

Note that KMail uses hidden sub-directories inside that directory, so you need to make sure to copy hidden directories as well.

For settings you will need to copy the following files:

~/.kde/share/config/kmailrc,
~/.kde/share/config/mailtransports, (since KDE 4.0)
~/.kde/share/config/emaildefaults and
~/.kde/share/config/emailidentities .

Your address book is usually stored in ~/.kde/share/apps/kabc/.

Calendar data is in ~/.kde/share/apps/korganizer

Be aware that some distributions use ~/.kde4 instead of ~/.kde/ for their KDE configuration data.

Look at the output of the command kde4-config --localprefix if in doubt.

From version 4.4 you may have some Akonadi-controlled entries that also need to be kept. Add to the above list -

Everything under ~/.local/share/
Everything under ~/.config/akonadi/.
~/.kde/share/config/nepomukserverrc
Everything under ~/.kde/share/apps/nepomuk/ (KAddressBook stores contact groups in Nepomuk.) 

If you plan to use an USB stick as transport medium for your data, be sure to format to a linux FileSystem.