You always want to read the ingredients when purchasing a new brand of pasta.
Ingredients to look out for are: eggs, egg whites, and sometimes "squid ink" for dark pasta varieties.
Common brands of pasta that are "accidentally" vegan are:
Barilla, Colavita, Divella, DeCecco (not yellow box line), San Giorgio (not their oven-ready line), Ronzoni (not the oven-ready lasagna and spinach fettuccine), & many store brands!
Moral of the story: There are plenty of vegan-friendly pasta brands at your local grocery store.
Always check the ingredients when buying new pasta, but you'll find plenty of options!