While not the game that brought the biggest change to the series, the entry that stood as the catalyst for change was 2011's Saints Row: The Third. If fans had missed an entry in the series before returning, they'd be thrown into something completely unfamiliar and unexpected, and if they had managed to stick with the series since the start, many were still dumbfounded by the number of changes made between entries.
Volition took its serious, GTA-competing gang saga identity and threw it out the window little by little until everything had been switched out for outlandish, alien-headlined slapstick chaos. Saints Row has been through quite a bit in its 14-year lifetime and it hasn't just seen changes to the storyline either.