At first, I absolutely hated any kind of RPG. I don't really know why...I didn't like the turn taking style, and I also hated random battles. I wanted to at least see the enemies so I could try to avoid them.
Then a friend introduced me to Chrono Cross. You could see the enemies, and for that I was glad. However, aside from that, something about this game...I just loved it! When my friend was tired, I made him let me start a new game and I played all night. I didn't get far though.
Soon after, that friend introduced me to Earthbound, which I loved. When I went to college, a girlfriend found out I liked Chrono Cross and introduced me to Chrono Trigger. Somewhere in all this, I found a new love for RPG style games...but I'd have to say those three are the top for me. You all have listed lots of other good ones!