They can be things that Square are probably never gonna do, if you like, or things in older FF's that have disappeared more recently.
What I would like to see is something like the "Journal" section in Kingdom Hearts, where the monsters are recorded, and other things like mini games are recorded and you can read more on the characters you meet.
I'd also like something that keeps track of enemies you've killed, and battle statistics, things like that. And after you'd finished the game I'd like you to be able to save all the cut-scenes to watch anytime (although they are supposed to be putting less of those in =( )