While waiting for any new replies to expand on what has been said before, there's a very good set of replies from the FAQ on the subject available here (with links to more within) specifically on the topic of the Greeks, and a related thread on the subject of Roman deification of emperors.

There are any number of ways to approach this question - in a literal sense, rituals, cults and sacrifices provide evidence of "real belief" (or really, practice). There's also the difference between literary representations of gods (e.g. Homeric) and real-life cults. In this comment taken from a discussion on Norse gods, though, I take the angle of what role "immoral" gods could fill in a tribal, patriarchal society:

Given the sparse sources on Norse belief, it is often useful to consider parallell mythologies. Thor, by most accounts the most widely worshipped Norse deity, shares many features with two other Indo-European deities with widespread cults - Heracles, and Indra. All three are immensely strong, short-tempered warriors who slay monsters (particularly, serpents) wielding blunt weapons and in general achieve their ends through violence or feats of strength; Thor and Indra are both associated with lightning (Indra's vazra, or club, is also depicted as a thunderbolt) - in the case of Heracles, it appears the storm-god role was absorbed by Zeus.

Moreover, myths and hymns associated with Heracles and Indra in particular share some important traits - most notably, they are warriors who are too powerful to be controlled or ruled (something stated explicitly by Indra in RV 4.42), even by divine forces, and by virtue of this, their use of violence and feats of strength allows them to transcend certain physical and/or social boundaries (Heracles, for example, kills his music teacher in one myth, and in another is absolved of his crimes by virtue of the great feats of his labours, among many other things). This seems to have been regarded as a sort of ultimate demonstration of masculinity and the role of the warrior (as opposed to the priest or the herdsman/peasant) in Indo-European cults.

The bottom line being that traits that may appear extremely unpleasant to us (short temper, selfishness, proneness to violence, using threats to get your way, drunkenness and so on) could in societies with a martial class, to whom raiding, plundering and warfare were culturally important activities, be seen as indicators of virility, manliness and even virtue.

It has been debated to what degree there was a "warrior class" in PIE society. Most probably it was an idealization; it's been suggested that it may have derived from unmarried men engaging in activities such as cattle theft to prove their worth, and being granted leeway in transgressing other social boundaries. Such behaviour could have been idealized by chieftains, proto-nobility and other classes of individuals who wished to increase their personal clout through violent destructive behaviour.

Famously these cults were rejected by Zarathustra, who apparently regarded the Vedic deva Indra and Rudra (Shiva) as demonic creatures unworthy of worship, to the point that the first line of the Zoroastrian creed, Yasna 12, is "I curse all of the Daeva", and it proceeds with a pledge to never again raid a Zoroastrian settlement, and to adhere to the practice of "ceasing the attack and putting down the weapon". So, the problems of such cults did not escape everyone, even in pre-history.