Answer: it depends.
Pasta is a very broad category of food. In this answer, we are strictly focusing on pasta. Not sauces, not cooking prep, not stuffed noodles. Just pasta. Store bought dry pasta is, in my experience, vegan-friendly 90% of the time. Egg pasta, not vegan. In fact, egg is consistently the only non-vegan ingredient in pasta. Fresh pasta from fancy Italian eateries is normally not vegan. Fresh pasta is frequently made with water, semolina flour and egg. Of course, you can also make fresh pasta without egg (and it’s delicious).
Result: check your labels. Dry pasta – likely safe. Fresh pasta – likely not vegan.