Touch the Dead
Seriously touch them. Mmmm. So meaty. Now that we have that out of the way, I can tell you about the Nintendo DS game, Touch the Dead. It doesn't have the honor of being the first zombie game for the DS, but it is probably the first rail shooter with them in it.
You play a a prisoner who has to fight his way out of jail and labs that are filled to the brim with the living dead. You shoot them by tapping on the screen with the stylus. You reload by dragging bullets from the lower right part of the screen to your gun magazines/chambers which are on the lower left. Make sure you make every shot count and don't get caught on a reload, since the dead will hammer your ass mercilessly. You can pick up extra health by shooting boxes and cabinets to see what is inside and get extra ammo for some of your guns as well. You get scored on hit percentage and what you're firing at, so be sure to aim carefully to score high.
It's a fun game, though short, as most rail shooters are. Worth checking out if you like zombies and shooters. It also sports a bitching cover by Arthur Suydam of Marvel Zombies fame.