I'm going to lead off with a quote from Tolkien's essay "On Fairy-Stories":
By the forging of Gram cold iron was revealed; by the making of Pegasus horses were ennobled; in the Trees of the Sun and Moon root and stock, flower and fruit are manifested in glory.
I think this sums up my attitude pretty well. The best fantasy, to me, is grounded in reality; most of the fantasy elements are not thrown in at random, but chosen to either heighten or subvert attributes which the realistic elements already possess.
For instance, I really loved the dire animals of 3E. A dire bear was still recognizably a bear. As such, it could partake of all our real-world knowledge of bears - both actual physical bears, and all the mythology surrounding them. Bears are already big and scary; this one was bigger and scarier. It didn't shoot lightning out its rear end and it didn't fly. It was just a bear with its bearness turned up to 11.
Or take undead. Dead bodies are creepy. They're cold. They frighten us on an atavistic level. They spread disease and make us sick.
So undead are really creepy. Their touch carries a lethal chill, and they inspire supernatural terror. They infect us with diseases like mummy rot; they sicken us by sucking the life out of us. Once again, undead are dead bodies with their deadness turned up to 11.
(Of course, there's another element of undeath that draws upon our real-world knowledge of corpses; in this case, however, it is the deliberate breaking of real-world rules that makes them effective. Dead bodies don't move around, and we all know this. So when a dead body gets up and starts shambling toward us, that's a profoundly unnatural thing, and we feel the impact of that unnaturalness.)
Horses are fast; pegasi are so fast they can fly. Bulls are tough and heavy and solid; gorgons are so tough and heavy and solid, they're made of iron and can turn things to stone. Big strong men are hard to put down; trolls are so hard to put down, they regenerate.
So, I tend to like monsters which fit that "like the real world, but more so" pattern. If something is going to get wacky special powers, those powers should heighten its existing attributes most of the time.
Not every monster has to fit the pattern, of course. There's nothing about snakes or lizards that suggests they ought to have wings or breathe fire. There's nothing about octopi that suggests they ought to suck out your brain. There's nothing about Jell-O cubes which suggests that they ought to ooze stickily through dungeon corridors, engulfing and devouring every... well, actually, you know what? Forget that last example. But I feel these monsters ought to be extraordinary and exciting, a step up from the less fantastical perils that adventurers normally face.
