I'm going through FFVII again at the moment because of its recent release on Steam and...well, at first I was really hesitant about going through it again because it's quite old now (about 16 years) and I've tried going through old games before and that tarnished some of the memories for me (I bought Baldur's gate on GoG and it has not aged well, at all imo). But FFVII is as good as it has ever been, the graphics aren't all that outdated because of the chibified anime style the characters have, but their edges are more noticeable now (I think Cloud's hair has more polygons then the rest of his body combined) and the nostalgia kick is ridiculously overpowering, I've been playing it with a grin on my face a mile wide.
I think Final Fantasy is a special kind of game series because, at its heart, it's a very simple series. There is a big bad who is threatening the world, enter heroes to stop him. Its themes are generally very shounen manga like, so you end up with the very skilled protagonist, the rival with an opposite temperament (compare cloud/barret, squall/seifer, zidane/steiner), the villain who's generally calm, but also manic (Kefka/sephiroth/Kuja) and the use of love triangles. (Cloud/Aeris/Tifa, Squall/Rinoa/Seifer, Zidane/Garnet/Eiko). They are simple enough that they can draw people in, but once in there are also levels of complexities that are implied or can be deduced. Look at the debate that surrounds who's the actual villain of FFVII (Sephiroth or his mother Jenova) just as an example.
The series has lost its way recently because the stories aren't as good or as in depth...the quality drops precipitously after Hironobu left, but then, that's just my opinion.