Remove any clams that are broken, or which do not close immediately if tapped. Soak the clams in cold water for several hours in order to loosen any internal sand.
In a large skillet, over medium-high heat, with at least 1/4 inch of olive oil, fry the zucchini until golden brown. You may need to do this in two or more batches; you want them crispy. Place on paper towels to drain, and keep warm. Lightly sprinkle with salt.
Bring a large pot of salted water to a boil.
In the same large skillet over medium heat sauté the garlic in the olive oil until golden. Add the clams and cover the skillet. Cook for about 5 minutes or until the shells open – discard unopened clams. Remove the clams from the skillet with a wire-mesh strainer or slotted spoon. Remove most of them from their shells – saving a few in their shells. Place all shelled clams back into the skillet with the remaining liquid.
Cook the spaghetti until al dente (two minutes less than the package recommends). Drain, and add the pasta to the clam sauce. Add the clams in their shells as well. Cook for 2 minutes. Add salt and pepper to taste.
Distribute the zucchini to the top of each plate. Serve immediately.