The AP Stylebook, The American Heritage Dictionary, The Chicago Manual of Style, the Merriam-Webster Guide to Punctuation, and The New York Times Manual of Style and Usage permit the omission of a comma between clauses joined by a conjunction if the clauses are short.
The Merriam-Webster Guide to Punctuation permits the use of a comma between clauses without a conjunction if the clauses are short and parallel.
The Chicago Manual of Style permits the stylistic omission of a comma between clauses joined by a conjunction.