Melkor and Sauron's goal

[Saraphim]

Morgoth was recorded as the most powerful of the Valar, at least at the beginning of the Silmarillion.

Power begs for corruption. It went to Morgoth's head and created within him the desire to be even more powerful. This need for strength is sated somewhat by dominating others, and that is exactly what Morgoth did, by corrupting the elves and creating his own little minions to do his bidding.

After that, it's only natural that he would want to dominate everyone else as well.

As for Sauron, well, his name before he joined Morgoth was Thu, and if I had that name, I'd be evil too. (*ba-doom-ching!*)

Anyway...

He most likely wasn't a very important little Maia, and wanted some recognition. So, he basically followed Morgoth's example.

[Legolas]

Desire to be the Creator.

[The Squatter of Amon Rûdh]

Which, although it is a natural desire in Tolkien's opinion, both of these characters take to extremes. Both are motivated by pride and a lust to take everything to themselves. Sauron is more of a possessor, but Morgoth, discovering that he can never rival the creations of Eru, turns to destruction and perversion. In the end he has no real goal other than to torture, warp and destroy the work of all those who hold Eru as the ultimate authority. Sauron resents Eru much less, but allows his pride and will to dominate to take complete control of his actions. In both cases, the end is eventually lost in the chaos of the means.

[Lush]

Oh, I personally always thought that Melkor read too much Marquis de Sade at an impressionable age.

Oh wait you want a serious answer.

A growing bitterness and greed that translate into a selfish desire for domination through violence. No sense of moderation. And de Sade.

[Mithadan]

From an old post of mine:

Tolkien's conception of Morgoth may have changed as time passed. He was originally one of a pantheon of "gods" each having their own sub-realm within the bounds of Arda (Manwe - air, Ulmo - water, etc.). These "gods" morphed into angelic Valar while retaining their pantheon-like characteristics of "elemental" power. Each had or assumed a role within the pantheon. Some of Tolkien's latest writings (the Osanwe-kenta for example) suggest that Morgoth's "role" was chaos. But rather than work cooperatively with the Valar, injecting his "wild card" into their works (the effect of chaos may have been the creation of wondrous variation in the natural world), Morgoth instead allowed his role to consume him becoming the ultimate egoist/hedonist. Instead of creating variation, he reveled in destruction and corruption. As Sharku suggests, he was not evil from the beginning but became evil through lack of restraint and utter selfishness.

Sauron suffered from similar flaws. Ironically, he is portrayed as a polar opposite of Morgoth. Sauron is portrayed as a lover of order. But in seeking to impose order in the world, he suffered from a similar lack of restraint which devolved into selfishness. Thus to impose order he uses many of the same instrumentalities employed by Morgoth to create chaos. The distinction being that Morgoth wanted destruction while Sauron wanted control. He too was not evil in the beginning but became so. As is reflected in the letter quoted by Sharku, there is no inherent evil in Middle Earth; nothing is per se irredeemable, though perhaps Morgoth and later Sauron reached a point beyond redemption.

This is from the "Inherent Evil" thread which can be found here.

[Theron Bugtussle]

Tolkien is just distilling evil from our real (and spiritual) world into his literary world. Why evil? Why sin? Why pride, envy, lust, fear? It is in the corrupted nature of fallen beings.