When we're attempting to portray most games in existence as "generic", we could most likely refer to a large portion of them. Whether adventure, action, or fps, each game can commonly relate in some fashion to another particular game or series. After all, a lot of the great titles that we have today came from inspiration while others were entirely unique.
There are, however, different levels of which we could define a game as being generic. While most would beg and differ that Halo is entirely generic, it was the first of it kind to employ cinematic and story-driven mechanics into gameplay while mostly taking a lot of notes from the Alien trilogy in terms of dialogue, encounters, and plot. So yes, while being defined as mildly generic, the game did possess some characteristics that made it itself, as followed by the later versions.
I believe that we could be harshly exaggerating the levels at which Halo could be defined as a generic series.
If you want to see actual titles that resemble their counterparts entirely, take a look at most MMORPGs out on the market today. How about that new Chinese FPS that was recently announced which looks exactly like Team Fortress 2 and Battlefield Heroes if they had a bastard child.
That is generic.