Powers and Abilities
As a spiritual entity, the Spectre cannot be slain in the conventional sense, though he can be destroyed. As Corrigan he was still very much the same as he died. But as Spectre, Corrigan's personality is influenced by the Divine Wrath (which has no personality of its own) and he becomes somewhat colder and distant as a result. Since WW II, the Spectre's persona has become increasingly distant from his humanity.
The Spectre's powers were reduced after the Crisis on the Infinite Earths, but he is still the most powerful human spirit on Earth. The Spectre and the physical body of Jim Corrigan can exist independently of each other. However, if they do not reunite within 24 hours, Corrigan's body will die and the Divine Wrath will return to the Ether until a new Spectre is chosen.
The Spectre is intangible, can fly, turn invisible, inhabit and animate inanimate objects, and sense the intentions of people in the place where they plan to carry those intentions out. The Spectre knows many secrets of the universe and its inhabitants, though even he is not omniscient. The Spectre can sometimes get glimpses into the future, although this is not without great difficulty. The only time he was given a long, vivid glimpse into the future was when God granted him one in order to warn the JLA and prevent universal destruction.
The Spectre can be injured or even slain by sufficient magic force, most notably the Spear of Destiny. Also, if the human host dies, the current Spectre will be no more and the human spirit and the Divine Wrath will separate, each going to his respective destination in the realms beyond life.
Powers and Abilities
Sauron was among the mightiest of the Maiar. Originally of Aulë's people, he acquired great "scientific" knowledge of the world: of its substances and how to use them. He would retain this knowledge throughout his tenure as the Dark Lord in Middle-earth, using it to forge the One Ring and construct his fortress of Barad-dur. Sauron also seemed primarily linked to the use of fire.
A flaming, lidless eye is often used as a representation of his will, and that eye is used as a symbol on all his armies' banners. As one of Morgoth's chief captains, his ability to tap into the fires in the earth would have been priceless. It seems reasonable to suggest that the forges of Angband had Sauron to thank, at least in part, for their effectiveness.
Among Sauron's chief powers were deception and disguise: In the First Age Sauron took on many forms. His battle against Luthien and Huan in The Silmarillion has him taking on no less than four separate shapes: his "normal" shape, presumed to be that of some kind of dark sorcerer, a great wolf, a serpent, and finally a vampire "dripping blood from his throat upon the trees" ("Of Beren and Lúthien," The Silmarillion). At the end of the First Age, Sauron took on a fair form to appeal to the Captain of the Hosts of the Valar and ask for pardon. In the Second Age, Sauron took up that fair form again and used it under the alias "Annatar" to deceive the Elves into creating the Rings of Power. The level of deception required to fool the Elves of Eregion must have gone beyond simply taking on a fair form. Sauron was literally instructing the Elves to make artifacts that while capable of great good, were ultimately purposed for his own domination and were imbued with power to arrest the natural order of the world. The Elves were unaware of who they were dealing with until the eleventh hour, and only narrowly escaped his trap. Centuries later, Sauron was able to deceive the Númenóreans and steer them directly to their own destruction under promises of eternal life. Such destruction is a testament to Sauron's manipulative nature and ability to twist the perceptions of his enemies.
An interesting dichotomy is set up between his deceptive nature and his symbol. While rarely appearing personally and deceiving all but the most wary, he represents himself as an all seeing eye that can pierce all disguises. Consistent with Tolkien's theme of evil being finite, wasteful, and self-destructive, Sauron's powers are gradually reduced as time goes on. After the Fall of Númenor, he is incapable of taking physical form for many years, and only then as a horrific Dark Lord, robbed of his fair form forever. After losing the Ring, it takes even longer for him to regain physical form, although by the War of the Ring, he has regained it.
In the movies, Sauron's weapon is a black mace used against the Last Alliance to kill both Gil-galad and Elendil. The mace is extremely powerful (either that or Sauron uses magic to strengthen his might), as it can blast back and kill entire battalions in one hit. In The Lord of the Rings: The Battle for Middle-earth II, it kills most units in a single hit, and even with the most durable, Sauron only needs a few hits (2 or 3) to defeat them.
The extent, nature, and specifics of Sauron's power are largely left to the imagination. Like his master Morgoth, he is capable of altering the physical substance of the world around him by mere effort of will (albeit to a far lesser extent).