I don't want to spoil anything here so I won't mention much about the series individually.
This list consist of a few carefully selected series from different genres that I believe are some of the best within their specific genres.
(Note that I did not chose one serie from each genre or anything along those lines. I simply chose my absolute favorites among all animes I've watched)
The reason that ef - a tale of melodies isn't there is because I felt that ef - a tale of memories was slightly better... but I feel like watching melodies before memories is a must!
There are multiple seasons of the same anime at some points (K-On! and K-On!! is an example) the reason for this is because I felt that both seasons were consistent in quality and neither was better than the other.