Some of my favorite pieces of music from the games:
FE4:
Disturbance in Agustria, I like both the in-game and arranged versions of this.
Door to Destiny
Lover 1
FE7
The Eight Generals, this one when I heard it particularly resonated with me in such a way, that it stuck with me for awhile.
Precious Things, probably my favorite overworld theme, although there are a few that compete with it.
Treasured Hope
A Knight's Oath, I like nearly every variation of this(FE1, 7, and 9), I didn't care for Shadow Dragon's too much, but it's growing on me.