Short of the SaGa series, this is probably my favorite Square franchise. With the sole exception of the fourth game, I've remained largely engaged in the events each game is following, and I enjoy specializing my units and pilots, how positioning is rewarded in later entries, and the very real advantages and disadvantages each weapon type presents. I also like that it is a mecha-focused series where generic mobile suits aren't the be-all end-all, with various other weapon platforms making (noticeably effective) appearances, such as the armored trains in FM3 or the Sea Kings from the original.
The dual scenarios presented in several of the games is refreshing as well, especially in the case of FM1 and FM3 where you can see the story from both sides of the conflict and recognize that characters that may otherwise appear to be simple 'bad guys', such as Liu and Grieg, aren't necessarily all that bad at all. Of course, there ARE characters like Driscoll, who, even after the addition of a second story line, seem bad just for the sake of being bad, but it's an overall nice touch.
I also appreciate -- scratch that -- outright ADORE that all of the games take place in the same world, and the events of one game do affect said world, even if it isn't shown directly in the story you are currently playing. The Alordesh Revolution, popularly mentioned throughout the series, for instance, is the setting of the second game and set off by the 2nd Huffman War, the focus of the first game. Further fallout from the 2nd Huffman War set in motion the general distrust that undermines Zaftra and sets part of the fourth game in motion. Furthermore, wracked with this constant warfare and economic struggle, the games also focus, in varying degrees, on technological ethics nations contend with in an ever escalating arms race, such as the sacrifice of human pilots to create superior AIs in the first game and human experimentation and engineering to create superior humans in the 3rd. It all melds together to create such a fantastic world that is not just a joy to experience through the events you are playing, but to research through other avenues provided to you, such as the people in cities and the network in the third game (even if it is tedious, on a good day, to navigate ._.).
Probably the thing I appreciate the most, though, was the 'final' game in the franchise. Front Mission 5's choice to abandon the series tradition of focusing on a squad during a single conflict to instead focus on a single person who lived through the events of all of the games made it a love letter to series fans, showing yet a little bit more of each war through new eyes and tying up loose ends, while focusing on an overarching story of friendships torn apart by war.