The world needs to be interesting, the story needs to be engaging, but most and I mean most importantly of the three the characters have to make you want to give a damn about them. Personally, I felt Final Fantasy XIII handled the first and last of what I mentioned fairly well, since every character significantly develops (Save for Snow, but hey, he's Snow) and Cocoon/Pulse were pretty awesome.
Gameplay is super important as well, so the battles or whatever have to be fun, or at the very least unique so people can still applaud that aspect. I like turn based, I like real time, I like random encounters, I like non-random encounters, whatever, just make it something I wouldn't hate doing for hours and hours. Final Fantasy XII I felt started off with great battle gameplay, it was interesting and new, but soon it wore me down, the computer was allowed to flat out cheat, and the License board let you do anything, which is good or bad. I typically prefer classes, like what Final Fantasy XIII and X did pretty well, even if eventually everyone could be every class, you were forced to rely on certain people for certain aspects.
Some of my favorite RPGs are most of the Final Fantasy series, specifically Tactics, that game is spectacular and probably my #1 pick with VI close behind and all the others (save for VIII, XI, and XII) are listed somewhere. They're fun to pick up every once and a while still. Old scool RPGs like Lufia And the Fortress of Doom hold a special place in my heart, Secret of Mana was awesometastic co-op RPG (why aren't there more of these?), Phantasy Star 4 (if you haven't played this old school gem, I recommend it. It's for Sega Genesis, and the other ones in the series are ok too, but this one is easily my favorite) and I really did like Pokemon, but I lost all interest after Silver/Gold. Persona 3 and 4 are two amazing games, with 4 possibly being my favorite game of all time right now, I'm not 100% sure, but it gets soooo many points for the story being solving a mystery, the characters being interesting, and the gameplay a 1-up from Persona 3's. Still, there kinda was a class system, as certain characters were the best at something and the worst at something else, though the gameplay was a lot of fun and I really get a kick out of Social-Links.
I just want to see were RPGs go now.