In the not-so-distant past, people were conservative about taking photos. It cost money to buy and then process film, and almost nobody took random photos of their everyday meals. As a result, when Mom took the camera out for some Christmas photos, there was often a partially exposed roll of film inside it, containing forgotten photos of birthdays or graduations from months before. Chances are that you've occasionally run across some old, forgotten film in a drawer or a box of a relative's personal effects. So what do you do with that old film - exposed or not - when you happen across it?
Film is a perishable item, with expiration dates typically a year or two out from when you purchase it. But did you know that expiration dates for film don't work like expiration dates for a jug of milk? You probably don't want to drink that milk beyond a few days from the "Sell by" date. A whiff of expired milk quickly tells you this isn't something you want to put in your mouth! Not so with film.
When it comes to film, how quickly it goes "bad" depends on the conditions in which it's been stored and the type of film it is. Sometimes it's luck of the draw, but often the results are surprisingly good. If the film has been subject to high temperatures in long-term storage, the results are likely to be very grainy with significant color shifts toward red, but you'll most likely still get pictures.
Professional and serious amateur photographers alike often store their unused film refrigerated, or even frozen, in order to maintain freshness and extend its useful life. But even film stored at normal room temperature can give excellent results far beyond the expiration date.
In general, black & white films keep the longest under normal conditions. You can find many examples on Flickr of photos shot on black & white film that are 30, 40 - even 50 years past expiration - often with little or no visible degradation in quality. Color film, on the other hand, will typically start to degrade within a few years of expiration date, but you can sometimes get usable photos from even very old color film.
Some kinds of film tend to store poorly and generally don't keep as well. Very high speed (ISO 1600 and up) and specialty infrared films tend to degrade faster due to radiation - something even cold storage can't prevent. Also, older integral films (Polaroid) rely on pods of chemistry that burst as the picture goes through the camera's processing mechanism. You can often find expired film for these cameras on places like eBay, but be aware that success with these films is becoming increasingly unlikely as the chemistry pods dry up due to age. Personally, I would avoid expired instant film and buy fresh, instead.
I sometimes get asked by people if they can still get old, exposed rolls of film developed. Unless the film has been stored in excessive heat or otherwise badly abused, you can usually recover images from those old rolls. If it's black & white, it's a near certainty the images will be decent! It's hard to put a price on old family photos, so I'd always suggest you give it a try. There are labs that specialize in rescuing old film, and some don't charge anything if the photos don't come out, so your risk is limited to postage. I have no experience with them, but here's an example of one such lab. If you want to try a local lab, be sure to take it to a pro shop; 1-hour lab chain stores aren't equipped to handle expired film.
What if you run across unexposed (unused) old film in a kitchen drawer of storage closet and want to try using it to take new photos? There's a lot of discussion about exposing old film in various online forums, so it's probably a good idea to Google your specific film. Generally, if it's black & white, I'd recommend just shooting it at the rated "box speed" (ISO 100, etc). In the case of color film, you may want to try shooting it at half the box speed; if it's ISO 100 speed film, for example, set your camera to ISO 50. If you want to read a discussion about compensating for old film, you can start here. If you don't want to mess with these adjustments, just stick it in your camera and shoot at the rated speed - it's not an exact science! In either case, be sure to let your lab know what you are doing so they can adjust their processing accordingly.
I wouldn't suggest using long expired film for any critical purpose. But there's no reason not to use it for novelty and creative effect. What do you really have to lose for trying? There are actually many people who routinely shoot expired film on purpose, and sometimes the results are quite beautiful. In the case of exposed film found among the belongings of family members, if there's a chance it contains irreplaceable memories, I'd send it in today and possibly revisit a moment that hasn't been seen by anyone since someone pressed that shutter button!