What word do we use to say that something is so easily available or commonly prevalent?

I would suggest abundant.

existing or available in large quantities; plentiful.

As you can see, the definition from Oxford Dictionaries shows that abundant encompasses what you want to say in one word. It is applicable to "things" like potatoes and gives the impression that they are found everywhere.

Commonplace seems a good fit.

commonplace adjective

​ happening often or often seen or experienced and so not considered to be special:

Electric cars are increasingly commonplace.

[CED]

synonyms include widespread, prevalent [Thesaurus.com]

Ubiquitous:

adjective

present, or seeming to be present, everywhere at the same time; omnipresent

The phrase "readily available" comes to mind.
http://www.dictionary.com/browse/readily

I had an example I was going to write, but then I said the words too many times in my head and now it sounds wrong. :(

If the subject is extremely common, "like water" fits:

informal : in large amounts - He spends money like water.

So, in the context of your examples, "potatoes are like water in that place" and "it's so cold over there, rum flows like water" (or "...they drink rum like water").

Another option is omnipresent:

omnipresent

ADJECTIVE

1. Widely or constantly encountered; widespread.
   ‘the omnipresent threat of natural disasters’

The noun form would be omnipresence.

Of course, widespread (from the definition) might work as well. (Though I'm not sure what the noun form of that would be.)

The previously provided Ubiquitous is the best general answer, but in some cases you may want to imply that a thing is not only commonplace, but can't be avoided, to the extent that it becomes humorous or even annoying.

In this case you could say that the thing is obligatory. This is often used to indicate that the item's presence is so strong that it's almost as if it were required by law.

"As we dined while traveled through the region, the obligatory potatoes began to pall..." "the obligatory XKCD comic..."

For non-food items, you can use "ten a penny" in BrEnglish, or its USEnglish equivalent "a dime a dozen" to indicate that something is readily, and cheaply available.

http://dictionary.cambridge.org/dictionary/english/be-two-ten-a-penny

be two/ten a penny UK (US be a dime a dozen)

: to be very common

​

glut ɡlət/Submit noun 1. an excessively abundant supply of something. "there is a glut of cars on the market" synonyms: surplus, excess, surfeit, superfluity, overabundance, superabundance, oversupply, plethora "a glut of cars"