Shmup- Shortened version of "shoot 'em up." This term is used for games like Thunder Force IV and Raiden II, where the goal is to clear stages of enemies as you control a ship/person/whatever, and battle the boss at the end of each stage. These games can scroll horizontally (left to right), vertically (top to bottom), or even remain on a single screen (like Asteroids and Space Invaders) or be isometric (Viewpoint, Zaxxon, etc.). They're generally broken up into several sub categories; scrolling/"old school" (Darius, R-Type, Gradius, etc.), manic/"bullet curtain" (Mars Matrix, DoDonPachi, the Touhou franchise, etc.) and "cute 'em ups" (Parodius, Gadget Twins, etc.).
There is a forth sub-category called "rail shooters" (Star Fox, Galaxy Force II, Iridion, etc.), but some argue that these aren't "true shmups." Of course, I say if it still plays like a shmup as it flies into the screen, then it's a shmup.