It depends on how the game implements levels. I generally enjoy RPGs, but I've been straying away from JRPGs because more often than not, they make grinding a requirement.
The important thing is that levels shouldn't constantly impede the forward momentum of the game. If I forget what the story is because I'm out in the desert killing crabs for three weeks, something is wrong.
The new levels should be used as a means to introduce new strategic options to the player, first and foremost. To me, the stats come secondary. Becoming generally stronger doesn't keep the game fresh like a new skill or ability can.
Ideally, an RPG should be paced so that if you are going to the right areas and doing a moderate amount of exploration or side quests, you are being constantly challenged, but rarely overwhelmed. Grinding should generally be reserved for completionists and people that want to headbutt their way through a game.
I like levels, the way most games these days use them. Even in my FPS's, they're there to give me access to new equipment or abilities, and that can keep a game fresh for months. That being said, the game itself has to be fun first.