Great example with the persona series, OD! I've had the same experience with each title in the series. I took a six-month break halfway through Persona 1 (the longest I've ever breaked and come back to a game) simply because I got worn out on the dungeons. Persona 4 I've now taken a three year break from... or maybe I should say I just stopped playing it one day. And 4 was infinitely more varied than 3.
It takes me back, in my mind, to the progression of the original RPG: Dungeons and Dragons. When that game came out, it was meant as a game, not a roleplaying experience. All the focus was on traversing dungeons. In my mind, that's still the purest form of the "game"; when there was actually a win-lose scenario. Role playing "games" aren't really games. They are assisted story telling tools, and their success or failure depends not on a condition of a mission but on the interaction between the GM and the PCs.
One of the reasons the progression from dungeon game to role playing game occurred was because the favored dungeons amongst players became those with character: usually involving a lot of traps, story elements, puzzles, and rooms that tied together either in purpose or through theme. Eventually that dungeon building grew into world building and by the time of AD&D we had the basics of what we know think of as the standard RPG.
For me, the same kind of scenario applies to a video game. As early as Zelda, gamers asserted through their buying decisions that they were more drawn to the kind of game where the dungeons had character, and the more story a game had, the more this became pronounced. In other words, the point of having a dungeon in most modern RPGs is not to provide an arena for the fighting system to take place, but to provide a tangential story told in the form of the dungeon's design, inhabitants, and the "experience" offered by that dungeon.
I could point to many many examples of this done well and done poorly, but briefly just to cover three:
1) Ocarina of Time: each dungeon represents an integral part of the history of Hyrule and a unique part of that land. To this day, that game probably has my favorite dungeons of all time. The variance in them is incredible and after each one you feel like you understand Hyrule a little bit more.
2) Metal Gear Solid: MGS is really a dungeon series, whether the dungeon is a Russian jungle or a frozen nuclear disposal facility. MGS1 is a game which takes place entirely within the corridors of a dungeon—even the outdoor areas are confined—and each room is a puzzle asking you to solve it in order to pass. And again, each room has its own personality and is tied in some way to the story of what's going on. It was one of the more brilliant uses of the dungeon concept.
3) Final Fantasy XIII: here's an example which, to me, shows that dungeons are not about how pretty they look but about how well they are designed. FFXIII is one long dungeon with no paths, no puzzles, no decisions, and monster fights set up for you in a straight line. It's not much better than the random dungeons of Persona because it doesn't involve the player in the dungeons: it becomes monotonous. It is essentially a pre-planned walk through an art gallery and if you get tired of the art (or aren't interested in it to begin with) you aren't going to enjoy the stroll.
Note to gamers: when someone shoots you in the face, they aren't "gay." They are "psychopathic."