Lots of collodion glass plate negatives are still good from the 1850s, when they were invented, and a goodly number of Daguerreotypes from the 1840s as well. Some of Fox Talbot's earliest kallitype paper negatives have survived, from the 1830s (once Herschel showed him how to fix them to remove the unreacted silver chloride).
So we can reasonably presume that a silver image can last, at a minimum, something like 200 years with so-so storage and no particular effort at conservation.
There is reason to believe that sulfide toned silver images will last more than 500 years (given that they can be demonstrated to be several times as durable against environmental stresses as plain silver images).
A polyester film base, protected from excessive heat and UV exposure, is likely to last a similar time -- 500 years or longer -- and the gelatin that carries the silver in modern films is similar to the connective material in leather, of which we have examples, still intact, dating back as much at 10,000 years. Likewise, cellulose paper can last at least 5000 years, as long as it's kept dry enough not to sustain mold growth. Acetate does a bit less well, and nitrate a lot less well, but even those can last a very long time if they're stored in conditions that don't encourage their inherent tendency to deteriorate.
So, it's reasonable to expect that, simply stored in ordinary containers in living and storage spaces suited to other items we live with every day, silver image, sulfide or selenium toned negatives and prints can last several centuries without further human intervention (they might not, depending on a bunch of factors we don't control, like natural distasters, as well as some we do, like initial processing conditions, but the materials are at least capable of this longevity). Add to that the fact that the most cursory examination will show (to the naked eye) that they carry a picture, and these materials are at least a little less likely to wind up in a landfill than some things...