Some people assert that after death, consciousness is suspended for a while before being reborn. This is called the in-between state (antarabhava). In Tibetan (Vajrayana) Buddhism there is much interest in the in between state where there are rituals and prayers to assist the departed toward a good rebirth. In Tibetan the in between state is known as the Bardo.
Some claim that this state lasts for seven days, others for 14 and yet others for 49 days. The in-between state is not mentioned specifically in the Tipitaka but we can assume that there is a pause of some duration before re-embodiment and the subsequent rebirth. The available fertilized eggs could not possibly correspond with the number of people who have just died and the consciousness seeking re-embodiment and thus some period of waiting must occur at least in some cases.
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 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