At what point in the path is one able to recall their past lives? In most traditions of Buddhism there is talk of the Buddha, or various Bodhisattvas talking about their past lives. 

At what point in the path to enlightenment is the ability to remember ones past lives gained?
Powers are generally orthogonal to insight.
Most enlightened people have some powers, but not all people with powers are enlightened.
The six higher powers (chalabhiññā) include the cessation of ignorance, leading to becoming an arhat and the knowledge of past lives.
Thus theoretically one can be an arhat but not have knowledge of past lives, if one isn't interested in pursuing such skills or vice versa. However, this is contentious, since popular lore expects arhats to walk through walls or be able to perform other special deeds, but the Buddha himself never solely equates powers with enlightenment.
Devadutta, the villainous cousin of the Buddha had lots of powers, including transforming himself into other beings through jhana cultivation, but he was no arhat even though he was only a short hop away from it - he simply had no interest in enlightenment. He was interested instead in profiting from the psychic and political powers of being a spiritual guru.

&quot;Remember one's former abodes&quot; (pubbe-nivāsanussati), that is, recalling ones own past lives;
&quot;Extinction of mental intoxicants&quot; (āsavakkhaya), upon which arahantship follows.

See Abhijñā or direct knowing
&quot;Are powers strictly necessary for enlightenment?&quot; is a separate question. While they can be a distraction keeping one away from enlightenment, after enlightenment they can become useful tools. For example, those on the Bodhisattva path are expected at some point to focus their training on attaining mind reading powers so that they may help others to liberation.
Yet, adherents of the Zen tradition would say enlightenment is very ordinary, it was never not there. Enlightenment is doing ordinary things in a most extraordinary way.
Before enlightenment, chop wood, carry water. After enlightenment, chop wood, carry water.
Watch &quot;Ten Oxherding Pictures&quot; on YouTube - https://youtu.be/bN126j4FH7g