No surprise, I also really like these things--they make you feel like a part of the character's life, you're involved. you're putting the effort in, even for little things. It's definitely possible to go overboard with this kind of thing, but there's a great balance that can be struck there.
Heavy Rain, for example, does this AMAZINGLY well, IMO. You spend the first few scenes as Ethan just starting your day and playing with your kids. It seems kind of weird and maybe even boring, but it serves a few purposes. One, you can get used to the controls in an atmosphere that's fairly casual (no one's threatening your life, your actions at this point don't really affect the rest of the game, etc). Two, you get to know the character--here's his life, his home, his family, the kind of work he does, etc. And three, you make emotional connections. YOU are doing your work for the day, YOU are playing with your kids, YOU are getting a birthday party ready. You connect to all of these thing in a personal way, and the bright colors and sunlight of this portion of the game coupled with those simple actions really enforces how much things have changed later on in the game, and they give even more weight to what you're later trying to accomplish.
Walking Dead, too, does all these things with simple actions, to the same effect. They could be put off to an automatic action, or a cutscene, but by having the player actively go through these simple actions, they feel like they're a part of the game and have invested something in the character's life and decisions.
Hmm...interestingly enough, now that I've written that out, I understand why some people didn't like Cognition's beginning. While it had those simple, small actions, you were thrown into the high emotion scenario before getting to know Erica and getting invested. That said, I personally really enjoy in media res openings like that, for that reason--you're immediately pulled in by the intense situation. So it has its pros and cons, but hey, thanks for this thread, darthkiwi, if for nothing else than giving me new insight on that particular criticism!