Here's some of my favorites that haven't been mentioned:
Aurora Quest: Otaku no Seiza in Another World is a PC Engine port/remake of a Famicom RPG. It is a wacky sex comedy RPG about a group of women a "God" has taken for his wives. They all hate men now and you have to convince them to join your team and fight against the evil ruler/deity/whatever. (I only barely understood the plot, sorry.) Pretty fun and a lot of goofy situations and townspeople. It's also got a nice mix of sci-fi and fantasy elements.
Dragon Knight 4 was mentioned, but DK II is an entirely different game with different gameplay and one which I like a whole lot better. The story and gameplay are a bit on the simple side, but it makes for a quick breezy adventure. The game is a first-person dungeon crawler with a strong ecchi theme. The townswomen have all been abducted and turned into monsters. You have to brave the dungeon, battle the creatures in order to turn them back into (half-naked) women, and stop the evil sorceress (?). It's very easy to play this game without knowing a lick of Japanese.
Did you know Rhapsody: A Musical Adventure had a sequel? There's... actually TWO sequels and a jigsaw puzzle game. This is the first sequel, for the PS1 (the second sequel is on the PS2), Little Princess: Maru Oukoku no Ningyou Hime 2. It's just as charming and light-hearted as Rhapsody, so if you liked that game, you'll probably like this one too.
Rune Jade is a Diablo-style action-RPG. It features anime cutscenes and a large cast of characters to choose from.
El Dorado Gate 1-7 is a serialized turn-based RPG from Capcom that features character design by famed Squaresoft artist Yoshitaka Amano. If you've ever wanted to play a game with characters that actually look like an Amano character sketch, this is the game.
After Armageddon Gaiden: Majuu Toushouden Eclipse is an RPG where you play as a monster with a party of other monsters. It reminds me a bit of Last Armageddon, but I like the battles in this one a bit more. But if you haven't played Last Armageddon (for the PC Engine CD amongst other platforms), it's also very good.