Depends, if you're after an online shooter you need no real connection [obviously]. I still think the single player games [Maybe apart from shooters, although there is the odd exception] have a degree of connectivity with the characters.
Mass Effect being one, and most definitely Halo. I agree with Heavy Rain having a character influence, but it was made with the single player in mind [again, obvious] so I don't see any real comparison between the two.
Even a game as silly as Portal [Woo Portal] has a connection with the character and user. I do think there is a good mix of games out there for both the Single-player and multi-player gamer in mind, Batman: Arkham Asylum, Mass Effect, Dragon Age: Origins, Heavy Rain, Portal, Half Life [Never gets old <3], Splinter Cell and on the multi-player aspect, the obvious shooters, which is the main attraction for multi-player, understandably as it creates a fast paced environment.
So as long as they keep the balance I don't see why it should change, I, for one, enjoy the mix of games available.
ps Nintendo please make a console to battle the PS3 and 360
Edit: Fallout too <3
Edit v2: Gahhh Red Dead Redemption <3