Quite a few for me. Armored Core series, Suikoden 2, FF tactics, Castlevania series (specially SOTN). There's probably more to add but I hardly remember the rest
I don't have favorite games so much as I have favorite franchises, but there are two names that immediately pop into my head when I think about favorite games.
First is Star Ocean 2. Can't say why exactly I liked this one so much more than other games but it sucked me in and didn't let go until I'd played it three or four times through.
Second is Final Fantasy IX, which was my introduction to Final Fantasy on account of me only having an N64 for most of the PS1 era. I have fond memories of my kid sister and I playing IX together and narrating the story to each other and passing the controller back and forth. IX's ending was also the first video game to ever make me break down in happymanly tears (don't you just love an unambiguously happy ending?).
Dunno what all the fuss about FF7 is, though. Played it once, thought it was too moody and angsty, haven't played it since. 8... bah, can't even remember about 2/3rds of the story in that one.
As for the aforementioned franchises... Kingdom Hearts, .hack, Super Robot Wars, and anything made by Nippon Ichi up to and including Rhapsody: A Musical Adventure (sue me, it's a guilty pleasure).
Okami is my all time favorite game... Well it's tied with the Legend of Zelda: Ocarina of time and Majoras Mask...
But all three games share similiar elements. What I love that they all do is really make every character you run into interesting and memorable. So much thought went into their dialogue and design. Like the juggling brothers from Zelda haha. Or the priestess Rao fro
Okami. Plus, all three have so many interesting dungeons/ temples.
otherwise I also love The World Ends With You ( it's my favorite ds game) and the Soul Calibur series. Taki and Lizardman are my main squeeze.
hmm..my all time favorite games...well..only one..but has many series..it's Super Robot Wars...a nice strategic game with many series mixed in to one...ahaha..