This question came up for me last fall (I believe while watching a Stanford CARDINAL (not Cardinals) game. There are only 27 Division I schools whose official school nickname doesn't end with a plural "s". A few are well-known or commonly in the news (Alabama Crimson Tide, Navy Midshipmen, Illinois Illini, Harvard Crimson). The rest (and also lists of Div II and Div III schools) are at this 2006 link.
Mental Floss has a quiz about professional teams whose names don't end in "S".