Designed by: Shouzou Kaga (original), Keisuke Terasaki (director), probably others
Influenced by: Strategy wargames
Series: There have been many Fire Emblem games, and most of them never made it to the U.S., although this is changing; the original game finally made it to America recently as a DS title.
Legacy: The Shining Force line of tactical wargames is obviously directly inspired by this. A more indirect inspiration was probably Tactics Ogre, which went on to directly affect Final Fantasy Tactics and, later, the Nippon Ichi (Disgaea) tactical JRPGs.
Fire Emblem is the first tactical JRPG wargame released, an inspiration for what would become an entire subgenre. It's a tile-based man-level wargame set on a grid with role-playing elements. Unique among computer games of the time, characters weren't interchangeable pawns but each of them unique, both in class and in stats. The more a character is used in battle the more experience he earns, making him subtly better in many areas.
Fire Emblem is a game of slow character growth. It's not hard for a unit to gain a level, but the primary advantage from this is each of his stats might increase by one. Every unit has its own level advancement percentage chance for each of its stats, information which is kept secret from the player, but even a character with great growth chances might just fail to gain a point in any one, or even any, of its stats, leaving him underpowered.
The Fire Emblem series are notoriously difficult games, so a bit of bad luck like this could make following battles rather harder. It's not unknown to reach the final battles of the game and reach opponents with defense stats so high that only one or two characters are capable of inflicting more than a few points of damage.
Fire Emblem (Screenshot courtesy http://hg101.classicgaming.gamespy.com/)
This is a bad situation for the player to be in, because if an enemy isn't killed in one hit, if it's in range it gets a free counterattack, and these same high-defense characters tend also to have high attack power. In Fire Emblem games, a character who runs out of hit points is usually dead forever. If this happens with a very useful character, the loss could be enough to make the game unwinnable in the end.
If you compare Fire Emblem to the third or fourth edition of D&D, the ones that emphasize tactical movement, they don't really look all that different from each other -- right down to the "support" for permanent character death.
Fortunately for players, the game does allow free restoring to the state at the beginning of a battle, so a favorite character can be saved... provided the player is willing to abandon all progress yet made in that fight. The ending even subtly changes based on who remains alive at the end of the game.
In some ways, Fire Emblem is more realistic than D&D. Magic users are relatively rare; most characters would be classed, in a D&D campaign, as some kind of fighter. Most weapons are non-magical, and even those that are have a limited durability. And most opponents aren't monsters but human characters.
D&D got its start in the rules of Chainmail, a not-dissimilar tabletop game which focused on the efforts of whole armies. It was Gary Gygax's idea to reduce the scope and add in fantasy characters and an overall "adventure" overgame to wrap the fighting. In Fire Emblem, the merest hint of that elder pastime can still be seen.