Thank you for the replies, everyone.
I can still remember the first time that I played the first Dragon Warrior (Dragon Quest) game. For some inexplicable reason, I was instantly enamored with and addicted to running around Alefgard with my character, beating up slimes and drakees, gaining experience, and upgrading equipment. I remember being thrilled at the time and utterly surprised that a game like this could possibly exist (I couldn't imagine that many people would have the same character-building fetish that I did).
Well over a decade later, I still can't get enough of these things, and I often still play the older ones on the Nintendo Entertainment System and Super Nintendo. My all-time favorites, however, are all on the Playstation. If I had to pick three that I thought were the deepest and most entrancing games, I'd say that Dragon Warrior VII (Dragon Quest VII), Grandia, and Star Ocean: The Second Story make the list.
I have to admit that I haven't played some of the ones released more recently, though, so it's possible that one or more of these games may be even deeper than the ones I have mentioned. Unfortunately, it seems that many of the games created these days are focused more on things like graphics and movie-like cutscenes than they are on gameplay. I guess this is what has sold the best since SquareSoft "revolutionized" the genre with Final Fantasy VII. Incidentally, I think Final Fantasy VII is an excellent game, but I also believe that it opened the genre up to a different customer base who enjoy modern role-playing games for entirely different reasons than those of us who have been playing since the days of the original Dragon Quest.
I also played an online text-based roleplaying game called DragonRealms for years. Trying to make my character as powerful as possible was my obsession throughout my college years, and studying often took a back seat to my training priorities. Having other people training characters in the game simultaneously and providing constant competition didn't help to lessen this obsession.
Unfortunately, I haven't had much time to play my beloved RPGs since I've started working professionally. I occasionally try to squeeze some time to play in on the weekends, but it's difficult to make progress with my characters at a rate that would satisfy me. On weekdays, I'm generally so exhausted after work that I don't feel like doing anything but eating a quick dinner and going to sleep. Yay for working life, eh?