(Including Action and Strat RPGs as well, only listing those I own and have played through significantly. I consider, to a degree, the Zelda franchise to be apply in the ARPG category, as much as Alundra, Secret of Mana, Landstalker, etc.)
In absolutely no particular order (after the generation breakdown)
8 Bit Gen:
Final Fantasy
Dragon Warrior 1-4
Ys I & II
Phantasy Star
Miracle Warriors
Crystalis
Zelda I, II
16 Bit Gen:
Final Fantasy 4, 6
Ys III, IV
Phantasy Star II, IV
Chrono Trigger
Landstalker
Shining Force I, II
Shadowrun (SNES)
Super Mario RPG
Secret of Mana
Lufia I, II
Beyond Oasis
Shining Force CD
Shining in the Darkness
Zelda III
D&D Warriors of the Eternal Sun
Light Crusader
Super Hydlide
Sword of Vermillion
32 - 64 Bit Gen:
Legend of Oasis
Shining the Holy Ark
Shining Force III
Valkyrie Profile
Star Ocean 2nd Story
Vagrant Story
Lunar Silver Star Story Complete
Lunar Eternal Blue Complete
Final Fantasy Origins
Dragon Warrior VII
Ogre Battle 64
Ogre Battle
Tactics Ogre
Final Fantasy Tactics
Grandia
Alundra
Suikoden I, II
Zelda V, VI
Paper Mario
King's Field I, II
Tales of Destiny
Tales of Eternia (false ToD II)
Legacy of Kain - Blood Omen
Aidyn Chroncicles - The First Mage
Current Gen:
King's Field IV
Zelda V Master Quest, Collector's Edition, IX, Four Sword Adventures
Grandia II
Grandia Xtreme
Skies of Arcadia Legends
Wizardry - Tale of the Forsaken Land
Final Fantasy Crystal Chronicles
Tales of Symphonia (expected, based on series history)
Gladius
Phantasy Star Online Ep. I & II
Phantasy Star Online Ep. III
Pokemon Colosseum
Summoner
Summoner (II) - A G-ddess Reborn
Breath of Fire V
Dual Hearts
Suikoden III
Handheld:
Final Fantasy Adventure
Sword of Mana
Zelda I, III (incl. Four Swords), IV DX, VII, VIII
Dragon Warrior I, II, III
Pokemon Red, Blue, Yellow, Gold, Silver, Crystal, Ruby, Sapphire
Final Fantasy Tactics Advance
Fire Emblem
Shining Force I
Dragon Warrior Monsters I, II (Cobi & Tara)
Golden Sun I, II
Lunar I (flawed but enjoyable)
Lufia III, IV (flawed, but enjoyable)
Mario & Luigi Superstar Saga
Phantasy Star Collection
Shining Soul II
Tactics Ogre - Knight of Lodis
D&D Eye of the Beholder (GBA)
Mario Golf GBC
Mario Golf GBA
Mario Tennis GBC
Crystalis
PC:
Betrayal at Krondor
Divine Divinity
Beyond Divinity
Gothic I, II
Wizardry I - VIII
Might & Magic I - V
Baldur's Gate I, II (incl. expansions)
Diablo I, II (incl. expansions)
Planetscape Torment
Eye of the Beholder I - III
AD&D SSI/TSR Golden Box games (all of them)
Elder Scrolls I - III
Dark Sun I, II
Darklands
Icewind Dale I, II (incl. expansions)
Realms of Arkania I - III
Ultima III - VII
Ultima Underworld I, II
Yes, I do realize that some of these games may be listed in the incorrect generation. That merely means, as in the case of the Lunars, Grandia, Skies of Arcadia, etc, that I got later upgrades/ports of them, not necessarily the original releases. Yes, I the distinct lack of later Chrono and Final Fantasy sequels is not an oversight in the least. I own them, played them, and disliked them. Mostly.