This is going to be quite a Square-heavy post I'm afraid, but considering they specialise in JRPGs, I think I'm within my rights here.
There was a guy on page 2 who wrote an extremely eloquent post about FFIX, and honestly I can't find a single thing in it to refute. The art direction, story, characters, world, gameplay, music... Everything just combined to make a truly wonderful experience. Play it. Vivi needs you to play it. And you wouldn't want to disappoint him now, would you?
I'd add VI, VII and VIII to this list as well (and IV as well, sue me). At least for me personally, these have all provided me with countless hours of enjoyment. Again, I've found the various elements just worked for me, and I became entralled with their worlds. Are any of them 'perfect'? It's so hard to quantify, games being subjective and all. VIII for example - I loved it, really loved it. But the Draw system annoyed me - anyone who's seen Spoony's review will know what I mean here. But did it kill my enjoyment of the game? No. I appreciate it for what it is.
I saw someone had mentioned Vagrant Story. I've got that, though I haven't played it for years. I remember it as being very good indeed. A bit different. And the art style wasn't what I was expecting, but was really atmospheric... Yeah, that's a good one.
And I'd add Secret Of Mana to the list too. One of the first JRPGs I ever played, and probably the one that got me hooked into the genre.
As far as linearity is concerned, I think it somewhat goes with the territory. The game is telling a story, and to do that it needs to progress through various points. This doesn't just apply to JRPGs of course. Uncharted is linear. It's also a cracking game. So the linearity of say FFX or XIII didn't really phase me - it made sense for what was going on. One is the story of a pilgramage, the other of a group evading capture. I'm not going to let this sort of thing get in the way of my enjoyment.
It all boils down to personal taste.