In the mid-80's we called them angst bunnies; then I started hearing DIB's (dress in black) and goth.
Actually, what I liked about 'Titanic' wasn't so much the romance (though I liked that, too) but the detail they put into developing even the background characters, and how they managed to portray the event as a tragedy, not just a big special effect or a bang-wow disaster. Then again, I'm a confirmed angst-bunny.