My forte in the field of FF music is in Final Fantasy 7, and for a long time I taught myself a lot of songs by ear. I have the Piano Book for FFVII now ($40, but well worth it...and any guesses that I've been learning piano?

) and here are some examples of what I can play:
-You...Who Are You?
-Me...Who Am I?
-Infiltrating the ShinRa Building
-FF VII Main Theme
-On Our Way
-On That Day, 5 Years Ago
-Farm Boy
-Waltz de Chocobo
-Chasing the Black-Caped Man
-Trail of Blood
-Gold Saucer
-Cosmo Canyon
-The Nightmare's Beginning
-Wutai
-Buried in the Snow
-Aerith's Theme
-Sending a Dream Into the Universe
etc...
Of course, there are others that I'm still part-way through learning (like Rufus' Welcoming Ceremony, Tifa's Theme, and Continue?). But I'm not going to even attempt to list those @_@
I too enjoy fiddling around on the piano and figuring out music from other songs and series. Also, I'm a learning harpist, and since harp sheet music is very similar to piano, it's fun to memorize pieces for the piano and play them on the harp. ^^ In some cases, it sounds better than on piano! (I kinda wish I had the option of a keyboard too, though...)
Edit: And addleboy, I very much agree with you. One Winged Angel is one of the toughest pieces in the whole FFVII book by far, and it's somewhere between 6-8 pages. @_@ I have a ways to go before I learn that one, that's for sure!
(...Okay everyone, you can rejoice now. I'm done ranting XD)