This is actually an interesting point of discussion for me, because I work in a supermarket, in the Operations section, so it's my job to clear out all the out-of-date food at closing time and chuck it in the big bins out back. We try and reduce wastage as much as possible, so usually we tend to reduce the price of items that are going out of date that day, by a small amount at first and then down to obscene prices in the last hour or so of trading each day (I've sold massive loaves of bread for 19p before, and sold three whole ducks in November for around £2 each when they originally cost over £15 - some woman took three home for the freezer, for Christmas dinner. Massive bargain for her...). However, usually, the food we chuck out is still fit for human consumption, and will be for days afterwards.
Everything that has a best before date on it can be preserved for much longer than the date. Either stick it in the freezer, or in the fridge. All of the food we chuck out each evening is still good quality and can be eaten, and indeed we often have people coming over the fence stealing the wasted food from the bins and taking it home (mainly students from my university, known as 'freegans'). Technically it's illegal for us to allow the food to be sold afterwards, or given away, and if these freegans get caught they tend to get a major bollocking from the staff member who catches them. But even so, that's only because we're doing our jobs. Really, most of us working at my place of work agree that the food should be allowed to be taken away by freegans, or should be given to the homeless, but we simply can't do it. It's completely illegal for us to do that, and we'd be liable if we did that and someone fell ill from bad food. So sadly, our hands are tied...
Regarding whether or not I'd eat out-of-date food myself, I would if it still looked alright and if it wasn't obviously bad. Most of it I'd be cooking anyway so any bacteria or whatever will die anyway, and if it's only in a few days then it should be fine. I have one egg left in the fridge that's about a month out of date, but I tend to check my eggs with the whole 'cup of water' trick to make sure they're still fit to eat, and this one egg still is even now. I have sausages and bacon in the freezer from October, and because they've been in the freezer all this time they're still good to eat. If my milk turns sour or my bread goes mouldy then of course I'll throw it away, but as long as it is still fit to eat then whatever the label says is irrelevant to me.