The last game I've finished (considering MMORPGs can't really be "finished") was a long time ago: "Dreamfall: The Longest Journey", it was a RPG on Playstation 2 or Xbox if I recall correctly. Interesting storyline, mixing technology-advanced setting with a more magic-oriented setting.
Favorite game of all time, I'd say Guild Wars. It has such beautiful art style, fun exploration of the map, great quest line and thrilling PvP arenas. Was a nice mix of MMO (in towns) and cooperative gameplay RPG.
Other games I really enjoyed on PC:
Knight Online (my first MMORPG),
Rappelz (a free-to-play MMORPG),
WarRock (8 to 64 players f2p Battlefield clone),
Gunbound (similar to Worms games),
Rakion (PvP arena with an archer, knight, mage, ninja and warrior),
League of Legends (support or mid usually),
...
Other games I really enjoyed on PC:
Knight Online (my first MMORPG),
Rappelz (a free-to-play MMORPG),
WarRock (8 to 64 players f2p Battlefield clone),
Gunbound (similar to Worms games),
Rakion (PvP arena with an archer, knight, mage, ninja and warrior),
League of Legends (support or mid usually),
...