Firstly, there are three different kinds of dates on your food. The sell by date is nothing to do with you: the shop is not allowed to sell it after this date, but this does not mean it has gone off.
As well as a sell by date, products have either a best before date or a use by date. 'Best before' means that it may deteriorate in quality after this date, but should not be unsafe unless it's rotten or covered in mould.
'Use by' means that it should not be unsafe to eat before this date, but this isn't guaranteed after.
Food does not magically go off when the date changes.
Expiry dates always err on the side of caution, ostensibly to stop anyone suing the manufacturer if they get ill eating food that was in date but gone off, but it's in their interests to be further on the side of caution than necessary, if it will make you throw it away and buy more.
There are some products that just don't go off. They are required to have a date, but you can ignore it. I have known people to come close to vomiting in disgust at the mere thought of eating tinned food a month out of date; I would happily eat tinned food twenty years out of date, so long as the tin is undamaged.
Things that won't go off:
- most dried foods like flour, pasta, rice etc, as long as they are kept dry
- anything in a tin, or a sealed jar or packet as long as the packaging is intact and unopened
- vinegar, vinegary condiments like ketchup, or pickled foods
- very sugary foods like honey and sugar. Jam is not sugary enough.
Things that are fine as long as they aren't rotten or mouldy, although they may not be as nice:
- fruit and vegetables
- cheese - if it has a small patch of mould, it is fine to cut it off and eat the rest
Dairy products other than cheese may be harmful if they go off, but you will normally be able to tell; check them carefully after the date.
Meat can be harmful if it goes off, and you may not be able to tell. How long you want to leave it is up to you: I wouldn't go more than two or three days for most meat, and no more than the day after with poultry. If it's past the date, be extra careful to cook it well.