Full disclosure: It wasn't long ago that I was the person described by Kimberly, always negative and energy draining. I was fortunate enough to live somewhere where my inability to communcate forced me to observe my own tendencies in a person, namely my next door neighbor.
Chances are this person you describe is unhappy herself and is drawn to you in an effort to feed off of your positive energy. If this is the case, she deserves your utmost sympathy. My advice is to repeat what she says with a positive spin.
Ex. "The world is coming to an end."
Response. "I feel so fortunate to enjoy life now, while I can."
Also, breathing. Deep breaths, through the nose and into your abdomen, not your chest. Don't flinch and don't give her the power to affect you. This also applies to the very real possibility that she is truly just a mean person and enjoys the power of affecting people. It's hard to accept that some people are just plain old mean, I know. Just don't give her the power. Remember, breathe.
Now's also a good time for a mantra. For years, mine was: And this too shall pass.
You, my friend, are a long distance runner. Nobody's more powerful than that.