Here is what Christian Teubner, author of The Pasta Bible, has to say on the subject: "Pasta dough consisting only of flour and water is made much better in factories than it can ever be at home." He says factories have better access to special varieties of flour and the machinery to manipulate it adequately. So technically, he leaves the door open for flour-and-water pastas, but he sure doesn’t provide any recipes for eggless pasta. Neither does Marcella Hazan or the authors of many of the other cookbooks sagging on our overburdened Italian cookbook shelves.
But Guiliano Bugialli, author of numerous Italian cookbooks including The Fine Art of Italian Cooking says pasta from the area around Genoa has traditionally been eggless. The pasta he presents is called trenette, which, he says, is commonly confused with tagliatelle or fettuccine (flat strips about 1/4-inch wide), but which is significantly different in two ways: one edge is curly and there are no eggs in the dough. And while he laments that packaged pasta is replacing fresh all too often in Genoa these days, he says he still knows people "of the older generation" who make fresh trenette.
The ingredients for trenette are 2-1/2 cups unbleached all-purpose flour, 1 cup of cold water, 2 teaspoons of olive oil, and a pinch of salt. The pasta can be made by hand, the same as a pasta with eggs, by making a well in the flour on a flat surface, putting the water, oil and salt into the well, and gradually incorporating the flour into the wet ingredients. Once the mixture has come together, knead it until you have a smooth ball.
You can also make it in a food processor. Once the dough is formed, roll it by hand or using a pasta machine. Then, if you want to be authentic - and who doesn’t? - you cut it by hand, using a knife on one side of each strip and a jagged pastry cutter on the other. A traditional dressing for this pasta is pesto.