More than any other aspect of it, the reason Earthbound wins out so much for me is because I enjoy just exploring the game world. It has a strong sense of place -- much more so than in nearly any other console RPG from that era. It's not that there's a lot of stuff to interact with in the game world, but every area conveys such a strong /mood/ that just moving through it feels meaningful. There's a very personal feeling to it, too.
(Maybe that's why I liked Contact so much, though -- it really gave me that too. The extent to which I enjoy moving through a game world really impacts my enjoyment of it).
I do want to note, to anyone who hasn't played the game before, that you don't need to grind at all after the first boss fight, and status attacks are useful on bosses. It's not a terribly difficult game if you apply a little strategy to it. Jeff's items are also quite useful (although Paula and Poo's personal skills, generally, aren't so much, which is the one thing I find really regrettable about the game). The battle system's really simple, but it's fast, and a lot of the enemies have unique... attack names/behaviors. They have personality.
Earthbound's also has my favorite audio in any RPG. Not just the soundtrack but the sound effects, even, and fuck I'm getting nostalgiasad now.