There are so many to pick, but I'll keep it fairly oldskool for now. Not in any sort of order, except Phantasy Star 2 is #1.
Phantasy Star 1 - the game that changed everything for me. Granted, some of the gameplay may seem dated (repetitive dungeons, simplified combat), but after only playing DQ1, Ultima 3 NES, and FF1, this game was just so absolutely mindblowing. It quickly became my favorite game of all time, just after seeing it at a friend's house, and made me want a Genesis for PS2 and 3, instead of the SNES I was dying to get upon its release. The graphics were awesome (animated monsters! smoothly scrolling 3D dungeons!), music was catchy, and I loved all the different planets you got to explore, as well as the different vehicles you can ride. Very challenging and extremely nonlinear as soon as you get your spaceship, too.
Phantasy Star 2 - my favorite game ever. Amazing setting, some of the best plot twists in video game history, extremely difficult dungeons.
Phantasy Star 4 - the offline PS games are my favorite franchise in all of gaming, and this is the perfect send-off (before PS turned into a despicable online game). The music is varied, the nods to the rest of the series (even the black sheep, PS3), the macro system (every turn-based RPG should have one of these), combination attacks, it's all here. Oh, and not to mention some awesome manga-influenced cutscenes.
Star Ocean: The Second Story - ridiculous amount of customization, all sorts of private actions that change around the ending, extremely fast-paced and fun battles, huge variety of gameplay, challenging postgame content. Only complains were the middling story and bad translation/dubbing. Actually the bad voice acting gives the game its charm.
Valkyrie Profile - I loved how the game's setup was different from your typical RPG, and the tale was extremely dark and depressing. The sidescrolling dungeons were a great idea (as my other favorite genre is 2D sidescrollers), and I like the combo-oriented battle system. Only problem was, getting the "good" ending was extremely obtuse and required a guide.
Dragon Quest 5 - probably the height of the DQ series. I love how the storyline spans the life of one person, from a young boy up till he gets married and has kids. Extremely epic in scope, in the way that only the DQ series can be.
Final Fantasy 5 - my favorite of the FF series. My first FF was 1, so a semi-throwback to that game, but expanding on the job system and allowing you to create combinations of different classes was a lot of fun. Game also had a great soundtrack.
Final Fantasy 4 - I'll never forget being absolutely blown away by the soundtrack, the first time hearing it. The game was also one of the first heavily story-based games I've played, so I'll always have great memories of it.
Chrono Trigger - It's a little too short, and gameplay a bit too simple, but the lush 2D graphics, amazing music (my favorite soundtrack ever), and cool time-travel premise makes up for that.
Skies of Arcadia - it's Kodama, how could you go wrong? I love getting and customizing my airship, the epic ship battles, the scope and breadth of the world, the different discoveries you made, the puzzle-filled dungeons, charming characters and back-to-basics storyline (especially at a time when more and more RPGs tried going the extremely complex philosophical route) Random encounters got on my nerves a bit though.
runners up: Live A Live, Dragon Quest 3, Dragon Quest 8, Suikoden 2, Mother 3, Ys Book 1 and 2, Ys IV, Ys: Oath in Felghana, Lufia 2: Rise of the Sinistrals, Shadow Hearts: Covenant, Baten Kaitos: Origins, Valkyria Chronicles, Final Fantasy 7, Final Fantasy 1, SoulBlazer, Terranigma, Ultima IV, Shining Force 2, Landstalker, Grandia, SaGa 2, Secret of Mana, Fallout 3, Planescape Torment, Tengai Makyo: The Apocalypse IV, The World Ends With You, Tales of Vesperia
