In Philip Pullman
's wonderful His Dark Materials
trilogy, daemons play an important part in the central plot
They are described by Pullman as an extension of a person's soul - a subconscious, if you may, that has a physical form, appearing as an animal. In the case of children, their daemons would not have a specific animal form but shift shape according to mood, then as they hit puberty, their daemon will change less and gradually assume a specific animal shape.
A couple of things must be said about Pullman's daemons. It is pronounced like the english "demon". Also, people mostly had daemons of opposing sex to theirs. You could talk to your daemon and he too you, but they rarely talked to other people, although they did sometimes. The shape your daemon took upon reaching puberty was of a large consequence - for example, if it decided to turn into a dolphin, or something like that, u were stuck living by the sea.
This brings me to another point concerning daemons which is that you couldn't separate yourself from your daemon - if you distanced yourself it became very very painful to live - like abandoning your heart. There was a deep love between human ad daemon. In death, one's daemon disappears - and in the underworld, it had to be left behind before crossing over to the isle of the dead. It was supremely rude to touch someone else's daemon, for daemons are very private. Although daemons could touch each other.
Another thing is to be said about daemons - they don't all manifest themselves in physical shapes - only people from certain worlds have this feature. although everyone has a daemon - inside. The protagonist of this trilogy comes from a daemon-displaying world - her daemon is called Pantalaimon.
What i found particularly intriguing about these novels was the fact that experiments were being made to sever children from their daemons, and the resulting cut would create energy which would be then utilised. Pullman manages to make you feel so much of what his characters are feeling - that the shock and horror of having one's daemon removed really hits home.