ablestmage said:

The giant spider that Gollum is talking about, that he calls "She" is not necessarily a capitalization of the pronoun "she" but instead perhaps an abbreviation of its name, Shelob. I'm not certain as to whether the gender of the spider is described except by this ambiguous reference (ambiguous as to whether it's an abbreviation or a capitalization of the pronoun)..

Shelob is definitely female, and while Gollum worshipped her (see below), I can't find a place where he referred to her as "She". In the narrative, Tolkien does, however:

But other potencies there are in Middle-earth, powers of night, and they are old and strong. And She that walked in the darkness had heard the Elves cry that cry far back in the deeps of time, and she had not heeded it, and it did not daunt her now.

Also:

There agelong she had dwelt, an evil thing in spider-form, even such as once of old had lived in the Land of the Elves in the West that is now under the Sea, such as Beren fought in the Mountains of Terror in Doriath… Shelob the Great, last child of Ungoliant to trouble the unhappy world.
Already, years before, Gollum had beheld her, Smeagol who pried into all dark holes, and in past days had bowed and worshipped her, and the darkness of her evil will walked through all the ways of his weariness beside him, cutting him off from light and from regret.

Here's what I would guess as a Middle Earth geek in good standing: Ungoliant was very powerful, and while of unspecified origin, seems likely to have been a very powerful Maia since she was able to trap Melkor (he had to summon Balrogs to rescue him). Shelob was Ungoliant's daughter, and thus at least partially of the same order of being. Since the Maiar were sometimes treated as gods in Middle earth, it's not surprising that Shelob would be referred to as "She" on occasion. For the few non-geeks who are still reading this: Sauron was a Maia, and his original boss was the evil Vala Melkor (the Maiar were lesser beings who served the Valar). Gandalf and the other wizards, as well as the balrogs, were all Maiar.

Glenn said:

I agree that Shelob is conclusively female. And there is a language "proof" of that fact. Tolkien is said to point out in a letter to his son that Shelob's name is formed from she plus lob from an Old English word, lobbe, meaning spider (Middle English loppe). This Old English word lobbe may also figure in the etymology of lobster.

Very interesting – thanks, Glenn!

I found some additional etymological tidbits on Wikipedia:

As Tolkien admitted in a letter to his son, Shelob "is of course only 'she + lob'," – lob being an archaic English word for spider, influenced by Old English loppe or "spider". The word is not related to "cob" nor "cobweb". Old English attercoppe (meaning "spider") is derived from atter meaning "poison" and coppe</em meaning "head"; Tolkien used "attercop" as well as "cob" and "lob" in The Hobbit, where Bilbo Baggins sings songs taunting the giant spiders in Mirkwood: "Attercop, Attercop, Old Tomnoddy" and "Lazy Lob and Crazy Cob".

I don't think that the article is correct about the non-relationship of loppe to "cob" or "cobweb" – and the The Free Dictionary confirms my suspicion.