Omitting "and" in a sentence

It's a rhetorical device called asyndeton, and you can find its definition (as well as those of other rhetorical figures) here.

Asyndeton consists of omitting conjunctions between words, phrases, or clauses. In a list of items, asyndeton gives the effect of unpremeditated multiplicity, of an extemporaneous rather than a labored account: On his return he received medals, honors, treasures, titles, fame.

I was taught that omitting the 'and' in such a situation was completely acceptable, especially in creative writing. The rhythm is much better without it. Leave it as is.