Rabbi Akiva says the root of the Torah is the Golden Rule, stated negatively — what is hateful to you, don’t do to your neighbor. Rabbi Hillel says the same thing but positively — love your fellow as your self. The Gemara also stresses the importance of emulating G-d’s positive character traits, such as being compassionate toward others. To paraphrase the Gemara, just as Hashem is gracious and merciful, so should you be gracious and merciful, bestowing free gifts to all. Just as Hashem is compassionate towards all creatures, we should be as well.
The book Compassion for Humanity in the Jewish Tradition, by fascinating chassidic author Rabbi Dovid Sears, is a good place to look for sources on this and similar topics. For example, the author of the Sefer HaBris, Rabbi Pinchas Eliyahu of Vilna, actually argues at length that love-your-fellow-as-yourself applies to non-Jews.