Would you believe I took a college class on vampires? Okay, let's get started.
Yes, I think our classic monstrosities can exist in this world. Allow me to illuminate the theories of their existence based on the notion of them existing today, here, and now. (And not, say, as a result of the events that gave us Morlocks or something.)
VAMPIRES - So, like I said, I took a class on this. And why not? It was fun! Your basic vampire boils down to some very basic traits to be considered as such. Namely...the vampire drinks blood and is alergic to sunlight. Most any other thing you've heard a vampire doing is a bonus, but not necessary. If you know anyone who also possesses supernatural abilities, RUN!! But in the meantime, the very basics of vampirism can be created by certain defects or hereditary oddities in the person's biology. Your craving for food is based on what your body tells you what you need. If your stomach says "WE NEED BLOOD!" you'd better be drinking blood or you're in trouble. Alergy to sunlight doesn't have to mean you turn instantly into a pyre. You could just be very susceptible to sun-related skin diseases, something which may be triggered by whatever biology makes you need blood. Can a person who needs blood to live and can't be out in the sun very much at all survive? Yes! They go out nights and visit hospitals regularly. Such people already EXIST.
WEREWOLVES - Of course, many people say that Lycanthropy is the werewolf disease, but we're looking for the I-change-into-a-freakin'-animal-here-folks disease. To which, the only way I can see a person become a werewolf in THIS WORLD is in a specific and permanent manner. That is, not a shape-shifting monster, but a dehumanization into a beast. Basing theories upon the notion of an ailment which produces appearances akin to a hairy beast (Lycanthropy), we take the idea further to an advanced stage of Lycanthropy. That is, one that affects the mucle development, the curvature of the spine, and other things. The man is made to find that four legs are better than two, and that developments have made him more adept to it. Suddenly, you have a hairy man on all fours. Provided said disease messes with things like his adrenaline and other brain chemicals, you can have him acting like a mad animal in no time. Can he survive? Only as a loner, unfortunately. Wolves have, legendarily, never accepted werewolves as truly their own, but as unnatural beasts. A man made into a beast cannot work in a pack.
ZOMBIES - See Max Brooks' Zombie Survival Guide on the realistic possible existence of the walking dead. I could make no better argument. And World War Z is an excellent support to their survival skills, such as they are.