This post was published more than a few years ago (on 2005-09-14) and may contain inaccurate technical information, outmoded thoughts, or cringe takes. Proceed at your own risk.
A good anime primer from MomGamer, good info on what to look out for if you have kids, but a good general introduction list for adults as well. There’s a second MomGamer column with more movies and TV series as well. Another good list is this Harvard Anime Society one, though it’s just a straight list with no reviews.