Wizards (the Istari) and Balrogs weren't exactly separate races or species: they're maiar: demigod-like spirits that might take the form of men or women, but don't actually have sexes in the traditional sense. But there were maiar who took the feminine form: Melian in The Silmarillian was a female maia (and had children - she was Elrond's great-great-grandmother).
Whether orcs and trolls were able to procreate (and thus, whether orc-women and troll-women exist) is an open question: it's established in The Silmarillion that Melkor couldn't create life ex nihilo: only Eru, who had the Flame Imperishable, could. So the only way to "breed" new creations was for Melkor to corrupt already living things.
In The Silmarillion,
For the Orcs had life and multiplied after the manner of the Children of Ilúvatar; and naught that had life of its own, nor semblance of life, could ever Melkor make since his rebellion in the Ainulindalë before the Beginning: so say the wise.
And in The Two Towers, Treebeard says,
Trolls are only counterfeits, made by the Enemy in the Great Darkness, in mockery of Ents, as Orcs were of Elves.
But contrary to the passage above about Orcs having life of their own, in The Silmarillion it's stated,
[...]that all those of the Quendi who came into the hands of Melkor, ere Utumno was broken, were put there in prison, and by slow arts of cruelty were corrupted and enslaved; and thus did Melkor breed the hideous race of the Orcs in envy and mockery of the Elves, of whom they were afterwards the bitterest foes.
So if this is the case, orcs and trolls didn't have sexes in the traditional sense: Melkor just warped whatever Elves and Ents he had in stock.
However, Tolkien himself went back and forth on this point, stating of the trolls so-called Letter 153:
As for other points. I think I agree about the 'creation by evil'. But you are more free with the word 'creation' than I am.* Treebeard does not say that the Dark Lord 'created' Trolls and Orcs. He says he 'made' them in counterfeit of certain creatures pre-existing.
And of creating life ex nihilo:
Suffering and experience (and possibly the Ring itself) gave Frodo more insight; and you will read in Ch. I of Book VI the words to Sam. 'The Shadow that bred them can only mock, it cannot make real new things of its own.
But in the same letter about orcs:
It is not true actually of the Orcs – who are fundamentally a race of 'rational incarnate' creatures, though horribly corrupted, if no more so than many Men to be met today.
So while the published works like The Silmarillion appear to establish orcs and trolls as corruptions of other living things (and thus, not truly beings in their own right), Tolkien was leaning more towards that being true of trolls but not of orcs.
And what's interesting is that Tolkien himself believed that orcs had female counterparts. In an unpublished letter to Mrs. Mumby, Tolkien stated:
There must have been orc-women. But in stories that seldom if ever see the Orcs except as soldiers of armies in the service of the evil lords we naturally would not learn much about their lives. Not much was known.
Dragons were also created by Melkor, but it's not clear to what extent they bred on their own (contradicting Melkor's stated power) or if they were all "bred" by Melkor himself: Glaurung is called the "Father of of the Dragons" and he had a brood, but it's not mentioned if it was simply an honorific (like the "Father of Disco" might be) or if he bred to create the other dragons.
There's nothing to suggest Wargs didn't breed, and if they did, there were females. There's nothing in The Hobbit to suggest all Wargs present were male.
Outside of Hobbits, Elves, Dwarves, Ents, Humans, and Spiders that you mentioned, there's also the Valar, which had male and female aspects: the named Valier were Varda, Yavanna, Nienna, Estë, Vairë, Vána, and Nessa.
There were also a great many beasts created by Melkor and by Eru: most things created by Melkor did not breed (and subsequently didn't have sexes), whereas most things created by Eru did (and thus, had both sexes).
But notably amongst Melkor's creations there were female creatures (or at least creatures referred to as female):
- the Great Spiders that you mentioned, where you had Ungoliant and Shelob, although it's not clear if Ungoliant was something created by Melkor, a Maia corrupted by Melkor, or something else entirely.
- there were also vampires, amongst whom, in the The Quest for the Silmaril, Thuringwethil is named the "woman of the secret shadow."
But like most things, Tolkien was loathe to get too worked up in the details and contradictions of his story, and whether X could breed but Y could not, and whether X had females or Y could not. In the same Letter 153, he says of the biological "difficulties" and peculiarities present in the Legendarium:
But I should actually answer: I do not care. This is a biological dictum in my imaginary world. It is only (as yet) an incompletely imagined world, a rudimentary 'secondary'; but if it pleased the Creator to give it (in a corrected form) Reality on any plane, then you would just have to enter it and begin studying its different biology, that is all.
And while this answer relies on Letter 153 and the unpublished letter to Mrs. Mumby, it should be noted that Tolkien didn't send letters for a reason: according to Christopher Tolkien (who compiled his letters), he left a note at the top of Letter 153 that said "Not Sent" and added "It seemed to be taking myself too importantly."
