Under ideal conditions - about 200 million years at least. In the salt, I'm not sure.

In the salt it's pretty similar. The salt caverns are basically just like the conditions where the early, easily-exploitable oil deposits ("gushers") were.

well it's been underground in similar conditions for a couple dozen million years, so I think a while

One time I heard the limited shelf life is by design to avoid consumers hoarding. Diesel OTOH fares better

No, it's because gasoline is not a very thoroughly refined chemical, so it basically has a bunch of aromatic rings, benzene, and all sorts of monomers floating around, that rapidly (~year or two) turn into varnish and other polymerized nastiness when they oxidize and crosslink. I believe gasoline was originally a refinery byproduct that was used because it was so cheap as a fuel.

Diesel and other heavier fuels generally are much closer to aliphatic hydrocarbons (straight chains, not aromatic) and so are much more storable, because aliphatic hydrocarbons have much less opportunity for oxidation (they're like saturated fat, i.e. much more stable).

You can get polymerization inhibitors to put into gasoline if you want it for long term storage, with the caveat that they produce some nastiness at the bottom of tanks that you'll have to avoid when pumping it out, and I think they can also slightly reduce the octane rating.

Diesel has limited shelf life: https://en.wikipedia.org/wiki/Microbial_contamination_of_die...

  Fuel companies state that untreated fuel will remain usable for only one year, after which fuel contamination ("the diesel bug") begins to appear

Typically, though, the diesel bug only happens in the interface between the water and the fuel itself, so if you have a proper filter and separator on the pumping system it won't be a factor.

Gasoline, when it goes bad, goes bad from top to bottom and is not recoverable through e.g. a centrifuge like https://www.youtube.com/watch?v=x4Fdu3e4gYw