In Devorah and Barak's song (upon defeating Sisra), part of the song went as follows (Shoftim 5:23):

'Curse you Meroz,' said the messenger of the Lord, 'curse you bitterly (you) inhabitants thereof,' because they came not to the aid of the Lord, to the aid of the Lord against the mighty.

The Talmud (Mo'ed Kattan 16A - English on page 59 here) brings two opinions of who or what Meroz is. According to one of the opinions, Meroz is the name of a star. So Devorah and Barak are cursing the inhabitants of a star (i.e. aliens) for not coming to their aid in battle.

According to here:

Hasdai Crescas, the great medieval Jewish philosopher, evoked the words of Psalm 19:2: “The heaven [or skies] declare the glory of God….” The rich cosmic landscape with all of its created wonders, is a testament to the artistry of its Creator...Crescas’ classic work, Ohr Hashem, originally published in Ferrara, Italy in 1555, contains an entire chapter where he maintains that the possibility of life on other planets is not in conflict with Jewish belief and Torah sources.

and from here:

Rabbi Chisdai Kerashkash, in his book Ohr Hashem (4, 5) explains that the possibility of extra-terrestrial life is not negated anywhere in Torah sources. The Sefer HaIkarim, on the other hand, quoted in Sefer HaBrit (1-3, 4), is of the opinion that there is no life on the stars and planets. The Sefer HaBrit himself argues, and agrees with Rabbi Chisdai. Similarly, the Chidah in Petach Einayim (on Tosafot, Menachot, 37a) is of the opinion that such life does exist.

Here is a link to the Ohr Hashem. According to the article by Aryeh Kaplan brought Adam's answer, it is Ma'amar 4, Drush 2.

Here is a link to the Chidah, (but he seems to be discussing two-headed sub-terrestrial human life.)

Here is the Sefer Habrit (Part 1, Ma'amar 3, Chapter 4). Please learn it, since I'm not sure I understood it correctly, but it appears he says that while life may exist, it will not be life we are familiar with. This is because the conditions are different there than they are here on earth. He compares this to sea-life. The Talmud says that everything that exists on dry land exists in the sea as well, but they are not exactly the same form. The ones in the sea may parallel the ones on dry land, but they're different because they live in a different environment.

He continues that it is impossible that there will be human-like aliens with free will, although they might have intellectual capabilities. According to Torah, only man was created with free will, not any creature lower (e.g. animals) or higher (e.g. angels) than him.

The Lubavitcher Rebbe (see here and here) said that “One who declares that there is no life besides on earth is limiting the Creator’s abilities.” And encouraged Professor Velvel Green to continue his work in this area.

The Lubavitcher Rebbe maintains that while life may exist on other planets, intelligent extraterrestrial beings with free choice do not exist. He appears to be differentiating between the capacity for intellect (a single trait) and an intelligent life form (the whole human package). [This may also be a result of a less than perfect translation]

Much like there are animals that can do things that are considered to be human traits, such as speak and use tools, so too there are non-human beings that have intellectual capacities. It is even possible that these non-human beings can surpass human capabilities. Angels, for example, have more intellectual capacities than humans (Maimonides Hilchot Yesodei Hatorah 3:9). However, free choice is a uniquely human capability that sets us apart from the the rest of creation. Free choice, according to Torah, is defining quality of intelligent life.

Free choice is only possible because G-d gave us the Torah. Without free choice, observing Torah and Mitzvot would be a sham. Therefore, when G-d gave us commandments, he gave with it the ability to truly choose whether to do them or not. It is because of the Torah that we have free choice. Since the Torah was only given to the Jewish people here on earth, we must say that any extra-terrestrial being does not have free will.

Civilized Societies are created by intelligent being with free choice. If aliens don't have free choice, they would not have civilizations.

See here for a summmary of the Lubavitcher Rebbe's view by Tzvi Freeman.