I've read the topic of whether or not God discriminates between Jews and non-Jews, but does God love non-Jews? Does it say anywhere that He does love non-Jews. I don't believe that God hates non-Jews or that Jews should hate non-Jews. I ask because someone is putting these questions to me and I am not sure how to answer all of them.
The Talmud in Megila (10b) relates: When the Egyptians were drowning in the sea, the angels wanted to sing God's praises. God silenced them, saying "My handiwork is drowning in the sea, and you want to sing?" This strongly implies that God loves all of His creations.
Yea, He saith: 'It is too light a thing that thou shouldest be My servant to raise up the tribes of Jacob, and to restore the offspring of Israel; I will also give thee for a light of the nations, that My salvation may be unto the end of the earth.
I think this answers the question, in that God wouldn't offer salvation to those He does not love.
I have learned with my rabbi that Gd's loving us is not an emotional experience for Him, as that would imply that he is by some chemical process or internal compulsion made to feel, which is in and of itself a physical construct and is inapplicable to Him, who is the prime cause of everything. Rather, Gd 'loves', (and expresses emotions in general), by way of his actions, and we ascribe emotion to his actions in order to understand His behavior in our minds
Organized society, generally speaking, functions well. There are many good-natured people in the world who enjoy healthy happy lives with their families and loved ones. It would seem that Gd absolutely loves them!
There is a mishnah that explicitly addresses this question (Although @ray's quote of Chovos haLavavos makes the point pretty directly.
הוא היה אומר, חביב אדם שנברא בצלם .חבה יתרה נודעת לו שנברא בצלם, שנאמר (בראשית ט), כי בצלם אלקים עשה את האדם. חביבין ישראל שנקראו בנים למקום.חבה יתרה נודעת להם שנקראו בנים למקום, שנאמר (דברים יד), בנים אתם לה' אלהיכם.חביבין ישראל, שנתן להם כלי חמדה.חבה יתרה נודעת להם שנתן להם כלי חמדה שבו נברא העולם, שנאמר (משלי ד), כי לקח טוב נתתי לכם, תורתי אל תעזבו.
He [Rabbi Aqiva] would say: Beloved is humanity, since it is created in the image [of G-d]. A deeper love is that it is revealed to him that he is created in the image, as it says (Genesis 9:6) "for in G-d's image He made humankind." Beloved are Israel, since they are called children of G-d. A deeper love is that it is revealed to them that they are called children to G-d, as it says (Deuteronomy 14:1) "You are children of Hashem your G-d." Beloved are Israel, since a precious instrument [the Torah] has been given to them. A deeper love is that it is revealed to them that the precious instrument of the world's creation has been given to them, as it says (Proverbs 4:2) "For a good lesson I have given to you; do not forsake my teaching."
G-d loves all of humanity, as they are in His "Image" and he let us know as much.
Yes, there is a parent-child relationship with Jews that differs from that of non-Jews. But this mishnah points out that this is not to the exclusion of Hashem loving all people.
Paraphrasing Yonah 4:10-11:
You Yonah are upset about the Kikayon which existed for a brief period and I [G-d] shouldn't care about the hundred's of thousands of people (non-Jews) that don't [yet] know their right from their left (infants).
Evidently, God cares about non-Jews.
That depends on who you ask. The mystics says "no" and the rationalist says "yes, G-d does love non-Jews." In fact, whole books are devoted to the topic. I will summarize the answer here.
In short, they are two views, each stands in stark contrast of the other. There is the traditional mystic view, the view of the 12-century Spanish poet Yehudah Halevi, and there is the rational view, the view of the pagan Greek Aristotle and his philosophical disciple Maimonides. First, we will examine the mystical view, the views of the Kuzari and Zohar.
The Mystical Approach: G-d loves only Jews
The Kabbalists (mystical followers of the book Zohar) felt that there was a real distinction between Jew and non-Jews. Even the nature of immorality was distinct, in that the soul of a Jews came from holiness while the soul of a non-Jew came from the idolatrous nations of uncleanliness and is not, “properly speaking, ‘man’,” says Bereshith 20b; cf. Amor 104b, Jethro 86a.
The Kuzari writes in 1:27:
“Any gentile who joins us [as proselytes] unconditionally shares our good fortune, without, however, being quite equal to us.”
Halevi then outrageously insists, that:
"If the law were binding on us only because G-d created us [and therefore available to all], the white and the black man would be equal, since he created them all. But the law was given to us [Jews] because He led us out of Egypt, and remained attached to us, because we are the pick of mankind. When the Israelites left Egypt they were all descendants of Abraham, Isaac and Jacob – there were no strangers among them."
This notion contradicts what the Torah itself writes about the mixed-multitude. Addonitily, it would be safe to assume that many Egyptians, including Canaanite slaves left with the Israelites during the Exodus.
On proselytes, he writes:
"Those, however, who become Jews [but are not born Jews] do not take equal rank with born Israelites, who are specially privileged to attain prophecy, whilst the former can only achieve something by learning from them, and can only become pious and learned, but never prophets."
The Kabbalistic view toward proselytes was no better. A gentile who converts acquires a new soul from heaven, but this new soul still lacks in spiritual caliber in comparison to Jewish souls. The Mishpatim 95b says it is a “great humiliation for the holy soul to enter into a ‘stranger’, namely into a proselyte. The Zohar even attributes the sin of the golden calf to non-Jews since it was of “mixed multitude.”
According to this view, G-d only loves the Jews. Kabbalistic thought was no better than the Halevian white 'biological' supremacy. Now we will examine the views of the rationalist. A more tolerant view.
The Rational Approach: G-d loves all of Humanity
This notion of rational observations stands in stark contrast to Halva’s view which claims that the only way to establish a firm belief in G-d, one must witness the occurrence of a miracle or divine revelation, which is at best, primitive thinking in nature. However in the modern age, the age of enlightenment, haskalah is born. Its founder was Moses Mendelssohn, a Maimonidean (follower of Maimonides). Mendelssohn placed a lot of emphasis on universalism. Thus all people are created equal and are all in the image of G-d. In regards to the messianic age, Maimonides wrote in his Mishneh Torah, Hilchot Melachim 12:1, that non-Jews “together with Israel will earn a comfortable living.” He also felt that Jews and non-Jews shared the same soul. It was not that G-d created two kinds of man. If so, were Abraham, Issac, and Israel (Jacob) inferior?
Contrary to the racist opinions of Halevi was Maimonides who believed in universalism. Maimonides was proud to be an observant Jew. He was also proud of the Jewish people yet, he did not think Jews were superior and that this was innate, instilled into the Jewish people alone. He felt that Jews were no better than other people, save the obeisance, observance, and obedience of the Torah, respectfully. This being the only distinction of the Jew. But anyone could convert. Ruth was a gentile who converted and Kings David and Solomon, as well as the Messiah, will descend from her. We see from here that gentiles have the same capacity to become the greatest leaders as those who are born to Jewish parents.
In short, Everyone is created b’tzelem Elohim, “in the image of G-d." Maimonides defines this image to mean intelligence, hence it is a duty to use one's intellect because that is the closest thing to G-d and it is the thing that separates us from animals.
According to this view, G-d loves everyone because everyone is made in "an image of G-d." Thus everyone is chosen.
There is a legend that tells us when Halevi died, he entered the trial before G-d, and in the heavenly court, he was greeted by Rabbis' Akiva, Meyer, Onkelos, and purportedly the great-grandmother of King David, Ruth – all of whom were proselytes. It is said that they all took their turns slapping him across the face and that he stood before G-d with scarlet cheeks.
 For more information please see Menachem Keller who stresses this point of universalism in his book Maimonides on Judaism and the Jewish people, and again in his article “Chosenness. Not Chauvinism: Maimonides on the Chosen People”
 It is noteworthy here to mention that Maimonides felt that the patriarch Abraham was only chosen by G-d only after he discovered G-d, independently through rational and observation. As the Midrash says, Abraham discovered G-d by studying the heavens, natural laws.