They come in two flavors. The Horatian ode (named for the classical Roman poet Horace) is regular each stanza has the same form. The Pindaric ode (named for the Greek poet Pindar) is irregular an inconsistent number of feet in each verse, for instance, or variation from stanza to stanza. (The terms don't accurately describe the odes of Horace and Pindar themselves, but that's the way they're usually used in English. Sometimes the Pindaric ode is called Cowleyan, after the English poet Abraham Cowley, who famously used the form in the late seventeenth century.)
Among the most famous English odes: Dryden's "Alexander's Feast," Keats's "Ode on a Grecian Urn," "Ode to a Nightingale," and "Ode to Autumn," Wordsworth's "Intimations of Immortality," and Allen Tate's "Ode to the Confederate Dead." Coleridge's "Dejection: An Ode" is a half-ironic use of the term.
In popular culture it's common to call any sort of poem an ode. Don't.
Note: This guide is still in the early stages of development.
Three question marks mean I have to write more on the subject. Bear with me.