There is never any need to hold to outdated grammatical rules. However, if you ever wish to play the pedant, or perhaps, determine what level of pedant you are, 'one another' is a construction to which you should attend.
Traditionally, English has had two separate reciprocal pronouns depending on the number of people being referred to. The phrase 'each other' should be used only when you are refering to two people: "My brother and I write to each other." If you wished to refer to more than two people you would have to use the phrase 'one another': "My family members write to one another."
Or... not. Tradition is a matter of recent history, not origin. The first emplacement of the each other/one another rule seems to have occurred in 1785, in George N. Ussher's work Elements of English Grammar. This is, in fact, just about the only thing that Ussher is remembered for, other than plagiarizing the likewise ersatz don't end a sentence with a preposition rule.
Before this, English speakers generally used these phrases interchangeably. Indeed, they continued to do so after Ussher's proclamation, despite centuries of uptight grammarians preaching the 'correct' usage. While both terms are still in use today, 'each other' has won the common usage contest, and 'one another' sounds a bit more formal and slightly archaic. Regardless, you may use either in whichsoever way you wish to.