The hollow noodle known as bucatini, a dried pasta made from durum wheat and water, is among the most classically Roman shapes; in the dish known as bucatini all’amatriciana, it is paired with tangy tomato sauce. See this Recipe André Baranowski
Tonnarelli is a a square noodle often made with eggs; many Roman cooks prefer tonnarelli for the peppery pasta dish called cacio e pepe and for partnering with certain tomato-based sauces. See this Recipe André Baranowski
Spaghetti can hardly be called a regional food anymore, but in Rome it is quasi-sacred, especially in that luscious cheese-and-egg-sauce pasta dish, spaghetti alla carbonara. See this Recipe André Baranowski
Gnocchi, whose name literally means “little lumps”, are dumpling-like pastas made, variously, from potatoes, semolina flour, or even spinach and ricotta; in Rome you’ll find plump gnocchi like the ones here, as well as gnocchi alla romana, which are usually flat disks or squares. See this Recipe André Baranowski