This is going to be pretty biased and personal, but here goes:
Path of Radiance. While I can't say I've replayed it the most or even played it the longest out of any game, I find myself always going back to it in my head for "man if only this FE game did its mechanic like this". It's a solid game with great music and story, making it likely my favorite in the series.
Sacred Stones. Definitely the one I've played the most. There was even a time I was playing it so much I fell asleep while playing only to wake up and see I was in the middle of a chapter with Colm opening a chest. At the time, it had all of my favorite mechanics of the FE series. Split class promotion, the trainees, even the towers and the skirmishes. I also love the story and the music of course. Lyon's Battle Theme is top tier material.
Awakening: Definitely a game I'll go back to at some point. Lot's of fun mechanics (and yeah okay a lot of the ones I love just happen to be shared with FE8) and fun characters.
Blazing Sword: I've had more time hacking this game than playing the game itself. I've never beaten it since the first time I did, but I really should at some point. There's a lot I like about it, gameplay, music, animations, etc. are all great and as it was the first FE game in the west, it seems to act as a testing ground for any new FE games. Just a solid game.
Shadow Dragon: A pretty cut and dry FE game. I know it's a remake of FE1, but it seems like (aside from making graphics better and making gameplay much smoother of course) it didn't try too hard to make it anything but and FE1 remake. Good music and fun multiplayer, but really not anything amazingly impressive.
Heroes of Light and Shadow: Had a lot of the same problems Shadow Dragon did. Really felt a lot like "Shadow Dragon BUT HEY YOU CAN MAKE YOUR OWN CHARACTER".
Fates (Birthright): I don't hate this game as much as others do, but I won't say I love the writing and certain mechanics that wedge themselves in. Some of the new mechanics, characters, etc were nice and while I can't say I plan to replay it, I'm happy with the fact that I played it the one time I did.
Ones not on this list and why:
FEHeroes: I love it and will likely be playing it for a long time to come, but comparing it to main series FE games would be pretty unfair.
FE4: While I did beat this, it was so long ago and in an only half-English patch that I don't remember a lick of it. I can't tell you what the plot was outside of what my brain could gather from actions. All I'd really be able to tell you about it is stuff that others can say just by looking at the game. I need to replay this one.
Binding Blade, Radiant Dawn, 1-3, and Conquest + Revelation: Haven't played these/Beaten them. If I did play them, it was only the first few chapters and cannot tell you how I see the game as a whole.