I am developing an iPhone App, but I will soon replace my old macbook with a newer one. Which content from the keychain should I migrate to be able to continue to develop the App on the new computer?
There is no need to mess with Keychain, Xcode's Organizer allows you to export and import all the certificates, private keys and provisioning profiles in one file.
Under Devices tab in Organizer select your team, click Export and enter file name and password. Then just double-click the file on other machine, enter your password and Xcode will import it.