This article is from the PGP FAQ, by Jeff Licquia firstname.lastname@example.org with numerous contributions by others.
Yes, you should sign each personal ID on your key. This will help to
prevent anyone from placing a phony address in the ID field of the key
and possibly having your mail diverted to them. Anyone adding or
changing a user id on your key will be unable to sign the entry,
making it stand out like a sore thumb since all of the other entries
are signed. Do this even if you are the only person signing your key.
For example, my entry in the public key ring now appears as follows if
you use the "-kvv" command:
Type bits/keyID Date User ID pub 1024/0353E385 1994/06/17 Jeff Licquia <email@example.com> sig 0353E385 Jeff Licquia <firstname.lastname@example.org>