At first I thought it was another type of sparrow, but couldn't find a picture of one that looked similar. I saw it several times at the feeder before I saw the male bird - a red-winged blackbird! Then I was able to make a positive ID. Here are better pictures of both birds courtesy of Wikipedia.
Male red-winged blackbird by Walter Siegmund
Female red-winged blackbird
In the second case, I kept seeing a rather nondescript grayish, brownish bird with no distinguishable markings. I saw it several times as well before I saw the male - a brown-headed cowbird.
Female brown-headed cowbird By Lee Karney
Male brown-headed cowbird
Cardinals are also examples of sexual dimorphism, although to me it's not quite as extreme and the above illustrations.
Female Northern Cardinal by Geoff Clarke
Male Northern Cardinal by Whaledad
Identifying birds is hard enough without having to remember that the male and female look totally different!