I'm almost finished with Record of Lodoss War (SNES) and have had a pretty good time with it. Then again, I'm a big fan of the OVA and anime television series. There's a lot of anime-based JRPGs I'm planning to play afterwards: Tenchi Muyo, Dragonball Z, Slayers, Jojo's Bizarre Adventure, etc. I can't say these are all great games (haven't played them yet), but at least as a fan of the series they come from I wll have a fun time.
Even aside that there have been some great games based on anime: Ghost In The Shell on PS1, some of the Macross shmups on Super Famicom, etc. And if you're just talking about games with anime-like visual styles and influences, there's Snatcher, Policenauts, Brave Fencer Mushashi, Fear Effect 1 & 2, Dragon Force 1 & 2, Odin's Sphere (and pretty much all Vanillaware games), Guilty Gear series, etc.