In between state
Some Buddhist schools assert that after death, consciousness is suspended for a period before rebirth takes place. This interval is called the in-between state (antarabhava). There are different theories as to how long this interval lasts. Some say seven days, others say 14 and yet others say 49. While Theravada Buddhism denies the reality of the in-between state, the Pali texts imply that there is an interval between death and rebirth. The Buddha spoke of the situation "when one has laid down the body (i.e. died) but has not yet been reborn" (S.IV,400). On several other occasions he said that for one who has attained Nibbana there is "no here, no there, no in-between" (S.IV,73), referring to this life, the next life, and the in-between state. He even said that in certain circumstances someone might attain Nibbana while in this in-between state. He called the individual who achieved this "a Nibbanized-in-between type" (antaraparinibbayi, S.V,69).
In the Vajrayàna Buddhism of Tibet the in-between state is called the bardo. Some Tibetans believe that reading instructions from a text called Liberation Through Hearing in the In-between State (Bardo Thodol) to a recently deceased person who is supposedly in this state, can help them avoid rebirth and attain enlightenment. This text is known in the West as The Tibetan Book of the Dead.
The Abhidhamma and the Classical Theravada hold that rebirth is always immediate with no intermediate state. Although there is no indication from the Suttas that directly references an immediate rebirth in all cases. It is only insisted upon in the Abhidhamma, which although part of the Pali Canon, is a later text.
There are a few other Suttas which suggest that there could be this intermediate state. One of the strongest indications of this is in the Metta Sutta which speaks of extending loving-kindness to 'bhuutaa vaa sambhavesii vaa' -- "to beings who have come to be and those about to come to be."
If there is an intermediate state (and the above suggests that there is) it would probably be reserved for just those higher or noble ones who are awaiting a good birth. For most, including animals and others, it is most likely instant.
See also: Gandhabba