I'll have to go with Triple Triad since you're pointing out the entire series, which makes me wonder what's this thread doing in this section anyways. Sure, some rules are stupid to say the least, but entire game is rather addictive, and fun. Same can be said for Chocobo hot, and cold, searching for Chocographs, and upgrading your Chocobo was addictive, needless to say it didn't stop there, the entire mini game lead to other sidequests, and one of the most challenging bosses ever.

As for Blitzball, I personally love sports, but I just couldn't get into it.