For the longest time, my favorite game in the series was Blazing Sword, but after playing more entries in the series i find it harder to pick a favorite. My current top 3 include Blazing Sword, New Mystery, and Fates.
Blazing Sword - I consider characters to be one of the most important things in a Fire Emblem game and FE7 probably has my favorite cast of characters in the whole series. Gameplay, i think, is also pretty good too with some exceptions like Battle Before Dawn, obviously. Story, however, i'm not too hot about. Also not a fan of having to play through the story like two or three times to unlock HHM. That can be pretty tiring. But those characters tho, that's the real selling point for me.
New Mystery of the Emblem - Probably the most difficult entry i've played so far (not including FE5). The gameplay here is the tops. Story i think is fine even with the inclusion of Kris. Sure I do find it annoying seeing them constantly being praised and whatnot but if i use my imagination and pretend that they're not there or that they're another character they become less obnoxious. Characters are okay. I don't dislike any of them, they just don't stand out to me. With exceptions of Castor, Caesar, and Linde.
Fates - Birthright was my introduction to the series and the one to make the most of an impact on me. Had I gotten Conquest as my first instead i probably would have found the game to be far too difficult and lose interest. That's why i went with Birthright instead, i read that it was more suited to new and casual players. Birthright also has one of my favorite cast of characters, just below FE7. Gameplay i think is not too special but not too bad, just a little above Awakening. Story for Birthright i think is passable. It's just a basic evil kingdom vs good guys story. Nothing too special. At least not as horrendous as Conquest's story. (also what's up with the back of the Birthright box having a gameplay screenshot of Conquest?)
- Conquest's gameplay we can all agree is top notch. But that's all i really have to say about it. Its story is a complete dumpster fire, and i'm also not too big a fan of the characters here with the exception of Inigo (or Laslow i guess). One really cool thing i liked tho were the cutscenes showing off the 3d models. Conquest doesn't have the same personal impact on me that Birthright had but it's gameplay is still among the best in the series.
- Revelation is better off treated as a sandbox game. At first i thought it was a decent game but on my second run of it, i found myself not enjoying it as much. When you get to the Valla section of the game that's where i think the game starts going down. I think the maps become too gimicky with the moving platforms and dragon veins and whatnot. The only way i'll play it nowadays is with busted units just cheesing through the chapters.
But let's not forget the music. Good lord, the music in Fates slaps HARD. Road Taken and Mingled Tears are among my favorite tracks in the whole series. Not to mention Rena Strober's work and the Endgame music. When I first heard those songs i had shivers going down my spine.
But overall, I have a sort of love/hate relationship with Fates.
Honorable Mention goes to Thracia 776.