I can't match the originality of most of the other posters, being a Liverpool fan. I do, however, have lots of wonderful memories, as a result, but unfortunately, at the opposite end of the spectrum, two of my darkest memories.
Like Elgar's Ghost notes, the modern game has changed out of all recognition and is no longer so enjoyable; or maybe I have just become a grumpy old man.
I follow a few other teams, overseas; Hertha Berlin, because I lived there once, Saint Etienne, because they were party to the finest football match that I ever attended (the 1977 European Cup Quarter Final, second leg), FC Nantes, because they were/are my mother's local team, etc.
My suggestion for great team names is Grasshoppers Zurich and, inevitably, Deportivo Wanka.
Okay, I confess, I looked the last one up; it is a real team, however, from Peru. Obviously twinned with Deportivo Moron, from Argentina.