How long after I have cooked chicken can I safely eat if stored in the fridge. Same day only? Next day? Within a week?
It's good for about 3-4 days in the fridge according to stilltasty.com. This seems to agree with my personal experience - I've left chicken in the fridge for a week and it definitely smelled "off" by then.
Make sure you wrap it, too. The link will say that it's OK as long as it's in any airtight container, but even in an airtight container, it dries out. I wrap it once in plastic wrap and again in foil and it stays reasonably fresh.
The offical food safety answer as I've seen it on various sites (such as stilltasty as recommended by Aaronut), 3-4 days.
My personal experience, I've had it last a week or a few days more.
I'll cook a large batch of chicken on the grill on a Sunday and my wife and I use it all week on salads at work, quick dinner wraps when we're in a hurry, etc.
It's not uncommon that I've been able to use the same chicken the next monday, without any off smell or slimy feel to the chicken, and without getting sick. But to be fair, I have an iron stomach, I wouldn't try pushing it past 5 days if you're susceptible to getting sick from food at all. I grew up in a house where food was regularly left on the counter overnight, so I've built up a tolerance.
That said, we store our cooked chicken in the bottom of our two fridge drawers, and for some reason that drawer half-freezes things. I suspect that's the reason I can get it to last longer than the recommended 3-4 days.