Spiders
There have been Giant Spiders in Middle-Earth from the beginning of Time. The Giant Spider's webs are extremely tough, and hard to cut. This does not show in The Hobbit, as Bilbo was using an elvish sword which he then called Sting. It was found by Frodo and Sam when fleeing Shelob, and the Elvish sword, Sting, cut the webs with ease, while Sam's sword hardly cut the threads at all. These Spiders could apparently talk, as they were heard talking to one another by Bilbo and recorded in his diary.
Winged Beasts
"A creature of an older world maybe it was, whose kind, lingering in forgotten mountains cold beneath the Moon, outstayed their day, and in a hideous eyrie bred this last untimely brood, apt to evil. And the Dark Lord took it and nursed it with fell meats, until it grew beyond the measure of all other things that fly; and he gave it to his servant to be his steed."
There were at least ten of the Winged Beasts, as one of the Nazgul had one shot out from under him by Legolas when he attacked the Company from the east bank of the Anduin River. They were like bats in that they had no feathers, but neither did they have any fur. They were quite naked.