Proper storage is the key.
A while back, I bought a big stash of Kodak EliteChrome 100(consumer Ekatachrome) with a 2001 expiration date.
The person before me kept it in the freezer from new, and that's where I've kept it since buying it. It's lost a little bit of saturation and a little bit of sensitivity over the years, but is mostly fine. The base fog has also increased a bit(unavoidable due to background radiation). I can actually quantify this, as I have a densitometer and can measure the DMAX of unexposed areas(slide film loses DMAX as base fog increases). BTW, Kodak stores master rolls(rolls that have been coated but not cut/perforated and packaged) in a salt mine where they have a virtually indefinite life.
Granted, when I'm talking about using old film, I generally process it promptly(within a few weeks at the most). The latent image is somewhat more susceptible to degradation than the film itself.
One last thing-disposables were crummy from day. I have photos from the early 2000s taken with them that were processed promptly and many of them don't look a lot different from the ones posted above. The usual methodology with those is to load 400 ASA film and use a fixed shutter speed of about 1/500 and an aperture of f16. This gives a decent daylight exposure(sunny 16) and also helps prevent motion blur. They typically have a single plastic lens focused to infinity or a little bit shorter, and the f16 aperture gives both decent depth of field and reduced spherical aberration from the poor quality lens. The lens, however, does introduce a lot of reflection and other issues that reduce saturation. The exposure also means that you basically can't get any get anything indoors unless you're right in front of the flash.