The only games I can think of that are 2D and a little bit in the anime style are Adventure Quest, Adventure Quest Worlds, and DragonFable which are all made by the same gaming company. They are fun games to play if you like this style but the graphics are not amazing but this is done in a cute 2D style.
Adventure Quest Worlds is also MMORPG with many character custom options and contains many aspects you see in most games such like armor, weapon, pet customs, quests and missions, instances with boss monsters with friends and ability to skills such like fishing.
More games in this style to me would be great because I like this type that is more realistic and relaxing.