I've played Sacred Stones, Awakening and half of Fates: Conquest.
Similar to Dragon Quest, I've tried quite hard to understand the hubbub around this franchise, but it's just not for me. I think the stories are generic, the characters are boring tropes (that repeat from game to game). I always feel like I'm watching some B-grade anime instead of experiencing a unique world with an actual story to tell. Combat in Fire Emblem games (particularly recently) rarely involves actual tactics, aside from moving a phalanx of your squad members slowly toward the enemy, while building up relationships so you can counter attack and one-hit-kill them.
The first S-RPG I played was FF Tactics, followed by Front Mission, and I found those stories/characters/world and systems are much more engaging (Front Mission DS is a fantastic version of the game, btw, with the full game and a second campaign). So when Awakening was getting all sorts of buzz, I was psyched for an entry among that caliber, and was sorely disappointed in what I found. For all its wordiness, I could summarize Awakenings' story in about two sentences.