Boktai series: These games were so near and dear to my childhood, especially 2. Really though you want the Solar Sensor hardware for the full experience, but I love these games too much not to plug them anyway. Emulating them is worth it over not playing them at all. And for the third game, you'd have to pick between original hardware or the translation patch anyway.
Castlevania: Aria of Sorrow - It's Castlevania. Also play Circle of the Moon and Harmony of Dissonance, but Aria is by far the best of the GBA installments.
Golden Sun 1/2: These games were way ahead of their time for how they designed a combat system that encourages you to use all of your tools and not just click basic Attack as if you gotta hoard your MP for a rainy day. Fantastic puzzles too.
Mother 3: Surely you have already heard of this game and do not need me to tell you to go play it. Have you not played it by now? Why not? Well, okay, if you haven't played Earthbound first, go do so, then play this.
Rhythm Tengoku: A wonderful game about pressing the A button. Sometimes you press the d-pad too. Translation patch.
Summon Night: Swordcraft Story 1/2: If you've ever played the classic 2D Tales games, these are excellent spiritual successors to those. There's a third game that's JP-only, translation patch is being worked on but it's been stuck in development hell for years...