The gameplay of FFIV hasn't aged particularly well. It's really basic compared to most RPGs these days, and though it introduced a lot of conventions used in later games, they were usually done more skilfully in those later games.
However, in terms of plot, it still works pretty well. For me the only large weakness in the story is the large number of fake character deaths. Square/Square Enix has released games with much larger plot holes since, so I'm willing to overlook this. The game has a well-told story with a coherent viewpoint and few obvious flaws, and even if a lot of things in the story are RPG clichés now, they weren't at the time the game came out.
All told, it's well worth playing and we're better off for having gotten it, although it would've been nice if it had had a better translation and a more faithful gameplay adaptation when we first got it on the SNES.