FFI doesn't quite hold up today.
Yet it's the one that started it all, and still worth playing once.
Yes, the original NES/Famicom version of FFII is one that should be avoided at all costs. The remakes that came after it, however, are absolutely not skippable.
The game gets a lot of flak for the way its leveling system is handled and its dungeon design punishes you for entering the wrong rooms, but the game's real glaring flaw that really killed the fun in the original version was the fact there was no auto-targeting at the time. And in a game like FF2 where the enemies' HP is averaged based on the current stats of your party, it is almost impossible to gauge your opponents' HP without hitting blanks (the result of another party member attacking an opponent that is already dead, thus wasting a turn.) The remakes - starting with Final Fantasy Origins - have improved on this tremendously just through fixing that one problem alone, and now battles can go smoothly without much room for error.
Looking past this flaw, however, FF2 has one of the darkest - if not THE darkest - storylines in the mainline series to this very day, complete with a compelling villain that ranks right up there with the likes of Kefka. He steals the show so much that title screens for the remakes not only featured him in Amano's illustration, but the game's writer - Kenji Terada - actually went out of his way to make a complete novel explaining his origins and how he came to be obsessed with conquest. Not to mention, he closely resembles David Bowie's character Jareth the Goblin King in the 80s fantasy movie "Labyrinth", which many believe the inspiration for this character's design is drawn from.
That aside, FF2 was also a first for many recurring concepts other installments would soon follow, which many seem to forget. FF2 was the first true character-driven storyline of its kind, giving us actual characters rather than unnamed individuals taking on a hero role. It was also the first to have supporting characters play an active playable role and temporarily join your party. It was the first to introduce us to not only the Chocobos, but also the recurring character Cid, the character class of dragoon through the character Ricard (who in a twist of irony, has a son named Kain, who has no relation to FF4's Kain), the mystic town of Mysidia, Leviathan, and iconic high-level monsters like the Behemoth and the Iron Giant.
But perhaps the game's biggest contribution was its style of gameplay, which in itself spawned an entirely new IP for Square called "Romancing SaGa", which has since become more polished with each installment (I highly recommend Romancing SaGa 3 if you haven't played it!). Unfortunately, the game's unique Password System was never carried over to other games, though a fun addition in its own right. Final Fantasy 6 would pay a small tribute to this sometime later in a particular scenario involving Locke, which only the most hardcore fans would catch on to.
Oh, and speaking of Final Fantasy 6, did I forget to mention some compositions in FF2 have a connection to it? Well, prepare to have your mind blown. The first few stanzas of the battle themes for FF2 and FF6 have a very similar melody if you listen carefully, and "Magician's Tower" also has some musical similarities to "The Magic House" from Final Fantasy 6. When the game was in development, "The Magic House" was an alternate version of the "Magician's Tower", but due to time constraints, Nobuo Uematsu scrapped this version, and would later use it for Final Fantasy 6 during the World of Ruin in the town of Jidoor.
All in all, my point is that FF2 is worth a try, as long as you're playing the remakes and not its original version, which I admit, much like Pandaemonium itself, is pure hell. Once you understand its gameplay and exploit its uses well, you'll have no problem getting into the series it inspired (and in a sense, birthed), the Romancing SaGa series. And you have to experience its dark storytelling at least once for yourself, because games like FF6 and FF15 were heavily inspired by this.