Did anyone ask the Buddha what their rebirth will be?

Buddha in the Patika Sutta tells about the rebirth of naked ascetic Korakkhattiya to Sunakhatta.

"I do not begrudge others their Arahantship, you foolish man! It is only in you that this evil view has arisen. Cast it aside lest it should be to your harms and sorrow for a long time! This naked ascetic Korakkhattiya, whom you regard as a true Arahant, will die in seven days from indigestion, and when he is dead he will reappear among the Kalakanja asuras, who are the very lowest grade of asuras. And when he is dead he will be cast aside on a heap of Birana-grass in the charnel ground. If you want to, Sunakkhatta, you can go to him and ask him if he knows his fate. And it may be that he will tell you: ‘Friend Sunakkhatta, I know my fate. I have been reborn among the Kalakanja asuras, the very lowest grade of asuras.’"

Then Sunakhatta goes to that naked ascetic Korakhattiya and tells all the things told by Buddha:

‘Then Sunakkhatta went to Korakkhattiya and told him what I had prophesied, adding: "Therefore, friend Korakkhattiya, be very careful what you eat and drink, so that the ascetic Gotama’s words may be proved wrong!" And Sunakkhatta was so sure that the Tathágata’s words would be proved wrong that he counted up the seven days one by one. But on the seventh day Korakkhattiya died of indigestion, and when he was dead he reappeared among the Kalakanja asuras, and his body was cast aside on a heap of Birana-grass in the charnel ground. ‘And Sunakkhatta heard of this, so he went to the heap of birana-grass in the charnel ground where Korakkhattiya was lying, struck the body three times with his hand, and said: "Friend Korakkhattiya, do you know your fate?" And Korakkhattiya sat up and rubbed his back with his hand, and said: "Friend Sunakkhatta, I know my fate. I have been reborn among the Kalakanja asuras, the very lowest grade of asuras." And with that he fell back again.

This is one of my favorites - Kukkuravatika Sutta: The Dog-duty Ascetic (MN 57)

The good part -

"Venerable sir, this naked dog-duty ascetic Seniya does what is hard to do: he eats his food when it is thrown on the ground. That dog duty has long been taken up and practiced by him. What will be his destination? What will be his future course?"

"Here, Punna, someone develops the dog duty fully and unstintingly, he develops the dog-habit fully and unstintingly, he develops the dog mind fully and unstintingly, he develops dog behavior fully and unstintingly. Having done that, on the dissolution of the body, after death, he reappears in the company of dogs. But if his view is such as this: 'By this virtue or duty or asceticism or religious life I shall become a (great) god or some (lesser) god,' that is wrong view in his case. Now there are two destinations for one with wrong view, I say: hell or the animal womb. So, Punna, if his dog duty is perfected, it will lead him to the company of dogs; if it is not, it will lead him to hell."

Ven. Ananda had the habit of asking Buddha the future destinations of people who passed away. So Buddha gave him the mirror of Dhamma so now you can decide this yourself.

The Mirror of the Dhamma

8. "But truly, Ananda, it is nothing strange that human beings should die. But if each time it happens you should come to the Tathagata and ask about them in this manner, indeed it would be troublesome to him. Therefore, Ananda, I will give you the teaching called the Mirror of the Dhamma, possessing which the noble disciple, should he so desire, can declare of himself: 'There is no more rebirth for me in hell, nor as an animal or ghost, nor in any realm of woe. A stream-enterer am I, safe from falling into the states of misery, assured am I and bound for Enlightenment.'"

9. "And what, Ananda, is that teaching called the Mirror of Dhamma, possessing which the noble disciple may thus declare of himself?

"In this case, Ananda, the noble disciple possesses unwavering faith in the Buddha thus: 'The Blessed One is an Arahant, the Fully Enlightened One, perfect in knowledge and conduct, the Happy One, the knower of the world, the paramount trainer of beings, the teacher of gods and men, the Enlightened One, the Blessed One.'

"He possesses unwavering faith in the Dhamma thus: 'Well propounded by the Blessed One is the Dhamma, evident, timeless, [18] inviting investigation, leading to emancipation, to be comprehended by the wise, each for himself.'

"He possesses unwavering faith in the Blessed One's Order of Disciples thus: 'Well faring is the Blessed One's Order of Disciples, righteously, wisely, and dutifully: that is to say, the four pairs of men, the eight classes of persons. The Blessed One's Order of Disciples is worthy of honor, of hospitality, of offerings, of veneration — the supreme field for meritorious deeds in the world.'

"And he possesses virtues that are dear to the Noble Ones, complete and perfect, spotless and pure, which are liberating, praised by the wise, uninfluenced (by worldly concerns), and favorable to concentration of mind.

10. "This, Ananda, is the teaching called the Mirror of the Dhamma, whereby the noble disciple may thus know of himself: 'There is no more rebirth for me in hell, nor as an animal or ghost, nor in any realm of woe. A stream-enterer am I, safe from falling into the states of misery, assured am I and bound for Enlightenment.'"

11. And also in Nadika, in the Brick House, the Blessed One often gave counsel to the bhikkhus thus: "Such and such is virtue; such and such is concentration; and such and such is wisdom. Great becomes the fruit, great is the gain of concentration when it is fully developed by virtuous conduct; great becomes the fruit, great is the gain of wisdom when it is fully developed by concentration; utterly freed from the taints of lust, becoming, and ignorance is the mind that is fully developed in wisdom."

12. When the Blessed One had stayed in Nadika as long as he pleased, he spoke to the Venerable Ananda, saying: "Come, Ananda, let us go to Vesali."

"So be it, O Lord." And the Blessed One took up his abode in Vesali together with a large community of bhikkhus, and stayed in Ambapali's grove.

http://www.accesstoinsight.org/tipitaka/dn/dn.16.1-6.vaji.html