Ah, top 5 threads! The bane of my existence due to my inability to pick favourites! I'll give it a shot, though! (And probably say very little and just talk about a few generic things. : P)
In no particular order:
Fire Emblem: Radiant Dawn.
Radiant Dawn was my first FE game and I'm really lucky because if I absolutely had to choose a number 1 it would be FE10. The plot is very engaging, the characters are great, the gameplay is really solid and the music is incredible. People like to complain about lack of support conversations but they're often really awkward and out of place and Radiant Dawn gave plenty of character development through base conversations and battle/boss conversations. While some characters absolutely were shafted (Vika, Aran, etc.) the writing was superb and Tellius definitely has the most engaging set of characters in the series. The only major flaw I have with FE10 is that sage caps suck. -_-
Fire Emblem: Path of Radiance.
I could list everything great about Path of Radiance but everybody know why it's great. Instead I'll complain that they replaced Maniac Mode with "Easy Mode" when Normal Mode already was the Easy Mode (like it is in FE10) and also complain that you can't turn off map animations. It also leaves a lot of loose ends for FE10 but I don't mind that.
Fire Emblem: The Sacred Stones.
The Sacred Stones actually has one of the strongest plots in the series. It also has a ton of replayability and some of the most memorable map themes:
Rise Above.
Determination.
Truth, Despair and Hope.
FE8 has a really great set of main protagonists too. The only problems are that it's also kind of easy and that the side/postgame content sucks.
Fire Emblem: Thracia 776.
Thracia is great because of it's ridiculous difficulty, mainly in your first playthrough, since enemy stats kind of suck and knowing about the cheese and how to stop it makes Thracia not nearly as difficult. It still has many very interesting mechanics (Fatigue, Capture, etc.), one of the most unique protagonists, a map theme for when you're losing, very good character diversity and the ability to make pretty much everybody really good while not breaking the game (because of capture and because pretty much everybody is broken in their own way. Except Ronan. Poor guy).
Fire Emblem: Heroes of Light and Shadow.
I wasn't sure what to put here but I think FE12 deserves the spot because it has really solid gameplay and very good class balance. It's the FE game where I've had to most think about unit positioning and it really tests you on harder difficulties. It's a shame that Kris killed FE3's story. However, it's still a really solid game and the original plot still exists. They just killed Marth's character and took away everything he did when they started FE's descent into self-insert hell. Also, unit balance kind of sucks and the latter half of the recruitable units pretty much all suck. :/