I have experienced almost every human emotion with Ecco the Dolphin 1 and 2 on the Genesis and SEGA CD. I am unsure how to describe it, but just the thought of being near the game is almost as strong a feeling as loving a person, I am that attached to the the series.
I have a lot of specific memories about it, from it and because of the game, and many can be linked to any really major part of my life now. It is pretty pathetic, I know, but what can I do?
It is of course my favorite game, but I do not think it is the best (VERY far from it) and I rarely recommend it to others based on how cutthroat the game can be.
There are others I have extremely emotional attachments to, like the original Sonic trilogy, the Sonic Adventure games, Virtua Fighter series, Skies of Arcadia, Virtual-On, Gunstar Heroes, Shining series, Panzer Dragoon, even weird stuff like Virtua Racing and Sakura Taisen. I just generally have a lot of love for most of their IPs.