Ear Worm: You try getting Geki!Tei out of your head. Bonus points if the dance has become reflexive. Yes, there is a dance. It even shows up in the manga as an occasional joke.
Fanfic Fuel: Some fanfics of the franchise included what if scenarios that fascist governments are in power and events that led to World War II start, forcing the various assault force divisions to disband due to the threats of war.
First Installment Wins: The original 1996 game was a huge critical and commercial success, hich spawned several stage musicals and OVAs, and the Imperial Combat Revue, the main characters from the first four games, is the group most people remember. Also, Erica and Gemini both get to be part of the main cast in both installments of Project X Zone. The advertisement info of Shin Sakura Wars that has been provided so far saying that the new characters are taking the torch not just because of the Time Skip but because all of the other Combat Revuesare apparently dead was pretty base-breaking, to put it nicely.
Moe: Most of the main female cast you can romance is this, but some stand-out examples include Erica and Rikaritta/Rosita.
"Seinfeld" Is Unfunny: While not as bad as what happened with the Tengai Makyou series (another franchise created by Ouji Hiroi/Hiroshi Adachi), the selling point of this franchise was playing a game that felt like watching an interactive anime series, especially in the 90s. Now, the games and the concept look dated compared to many other games that took the concept and expanded upon it.
Tough Act to Follow: Let's say Oji Hiroi's career took a serious hit after the franchise was finished (along with Tengai Makyou) since he hasn't been able to create another successful game or franchise again. The last game he worked was an Otome Game for girls which is basically a Follow the Leader version of Hakuouki and it's even more obscure than his previous works. On the other hand, this was averted with the rest of Red Entertainment, since they're still making successful games, like Gungrave.