Has no one mentioned Aria di Mezzo?!!
omg...

After that it would probably be:

FFX ending theme (makes me weep every time)
Seto's theme (FF7)
Terra's theme on Piano
To Zanarkand
Lenna's theme
The Successor (FFVIII)

and so many more...I also love the 'funny' or weird melodies, like the Phantom Train of FFVI or the Honey Bee Inn of FFVII (oh and the theatre music, hehe).