okay ; OK ; O.K.
Each of these is okay. Although OK predominates in highly informal contexts, okay has an advantage in edited English: it more easily lends itself to cognate forms such as okays, okayer, okaying, and okayed. The term is a casualism in any event, but okay is slightly more dressed up than OK. Some purists prefer OK simply because it’s the original form. It is, after all, the most successful Americanism ever—perhaps the best-known word on the planet.
A few publications, such as The New Yorker, prefer the periods—e.g.:
“It’s O.K. Take your time.”
Arthur Miller, “The Bare Manuscript,” New Yorker, 16 Dec. 2002, at 82, 91.
For more on the presence or absence of periods,
Garner’s Modern American Usage, Bryan A. Garner