As you probably know, the gods are ubiquitous in Homer's Iliad. Moreover, they are constantly interfering in the affairs of people and fighting each other even. In fact, there is so much that the gods do that it is hard to know where to begin. In light of this, I will give a brief snapshot of the gods and who they favor.
First, Hera (after being slighted by Paris in the myth of the judgment of Paris), sided with the Greeks. She even tries to trick her husband, Zeus to favor the Greeks. For the most part, Zeus stays impartial.
Second, Artemis and Apollo side with the Trojans. For instance, according to mythology, Artemis would not give favorable winds to Agamemnon and the Greeks to sail to Troy, until Agamemnon sacrificed his daughter. Also Apollo offers great succor to the Trojans, and for this reason the Greeks are nearly at the point of sailing back (he sends a plague for nine days), because Agamemnon will not give back the daughter of the priest of Apollo.
Third, when Paris should have been killed by Menelaus in their dual, Aphrodite whisks away Paris to save him. This is completely unfair, but Aphrodite cares for her favorite.
Another example comes from the dreams and visions given to Andromache, which are never heeded. This is a rather horrible lot to have, if you think about it.