Conventional pasta is durum wheat semolina and contains gluten. Rice, corn, chickpea, lentil and 100% buckwheat noodles are gluten free. Soba is the trap, because most soba sold is a buckwheat-and-wheat blend.
The noodle aisle is unusually forgiving once you know which base grain you are looking at, with one systematic exception.

Soba is the systematic exception. Buckwheat is not wheat and is entirely gluten free, but pure buckwheat soba is difficult to make and comparatively rare. Most soba is cut with wheat flour, often the majority of it. Juwari soba (十割) is the 100% buckwheat designation. Anything else should be assumed to contain wheat.
Asian noodles otherwise divide cleanly: rice noodles, glass or cellophane noodles (mung bean or sweet potato starch), and shirataki (konjac) are gluten free; udon, ramen, somen and most wonton wrappers are wheat.
Cooking water is the cross-contact issue people underestimate. Gluten-free pasta cooked in water that previously cooked wheat pasta picks up measurable gluten. In a home kitchen use fresh water; in a restaurant it is a question worth asking directly, because a shared pot is the most common way a gluten-free pasta dish fails.
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Sorted by what the answer actually is, rather than alphabetically — because the useful question in a shop is “which pile is this in.”
Wheat.
Wheat noodles.
Small pasta made from semolina, not a grain of its own.
Rice-shaped, but wheat pasta.
Usually buckwheat cut with wheat. Only juwari (100% buckwheat) soba is gluten free.
Rice and water.
Mung bean or sweet potato starch.
Konjac root.
Legume flour; check the blend for added wheat in some brands.
The most common gluten-free pasta base.
Usually not. Buckwheat itself is entirely gluten free, but most soba is made from buckwheat blended with wheat flour. Look for juwari soba, the 100% buckwheat designation, or a gluten-free claim.
No. Couscous is very small pasta made from semolina wheat, not a grain in its own right. Pearl or Israeli couscous is the same thing at a larger size.
No. Gluten dissolves into the cooking water and transfers to whatever is cooked in it next. Use fresh water at home, and ask about a dedicated pot when eating out.
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