Super Robot Taisen: Original Generation 1-2
Strategy RPG mecha series with a distinct combat system involving multiple weapons of various ranges and effects mounted on each unit. Very dramatic and cinematic plotlines.
Zone of the Enders: The Fist of Mars
Another SRPG, with a Gundam-esque plot and a unique and slightly bizarre first person combat system where you manually dodge or aim attacks.
Metroid: Zero Mission
Probably doesn't need to be mentioned, but one of the finest of the series and in my opinion better than Fusion.
Monster Rancher Advance 1-2
The forgotten monster training series, with a more literal take on it. Feeding, training, disciplining, entering in tournaments and keeping your monsters well. Going bankrupt is a distinct possibility if you fail to win tournaments and earn prize money. The battle system takes time to get used to, as it is based on distance and positioning to determine attacks so a level of personal skill with the controls is necessary. Gets sad when monsters get too old and need to be retired.
Wario Land 4
Surprisingly good platformer with interesting mechanics and frankly nightmarish enemy and boss designs.
Games previously mentioned or that likely don't need a writeup;
Final Fantasy 1-6
Final Fantasy Tactics Advance
Castlevania: Aria of Sorrow
Mega Man Battle Network
Fire Emblem / Fire Emblem: The Sacred Stones(♥)
Tactics Ogre: The Knight of Lodis
Shining Force: Resurrection of the Dark Dragon
Advance Wars
Golden Sun
Tales of Phantasia (Though I prefer the SNES version)
Kirby: Nightmare in Dreamland
Games that may interest you but I have limited personal experience with, or are divisive;
Boktai: The Sun is in Your Hands
Yggdra Union: We'll Never Fight Alone
Summon Knight: Swordcraft Story 1-2
Rebelstar: Tactical Command (Simplified, linear X-COM)
Scurge: Hive
Robopon (Pokemon-like monster collecting)
Astro Boy: Omega Factor (Yeah, trust me)